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THE JARROW AND TURNBULL SETTING REVISITED International Journal of Theoretical and Applied Finance Pub Date : 2024-03-13 THOMAS KRABICHLER, JOSEF TEICHMANN
We consider a financial market with zero-coupon bonds that are exposed to credit and liquidity risk. We revisit the famous Jarrow & Turnbull (1995) setting in order to account for these two intricately intertwined risk types. We utilize the foreign exchange analogy that interprets defaultable zero-coupon bonds as a conversion of nondefaultable foreign counterparts. The relevant exchange rate is only
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INFORMATION-BASED TRADING International Journal of Theoretical and Applied Finance Pub Date : 2024-02-28 GEORGE BOUZIANIS, LANE P. HUGHSTON, LEANDRO SÁNCHEZ-BETANCOURT
We consider a pair of traders in a market where the information available to the second trader is a strict subset of the information available to the first trader. The traders make prices based on information concerning a security that pays a random cash flow at a fixed time T in the future. Market information is modeled in line with the scheme of Brody, Hughston, and Macrina. The risk-neutral distribution
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LOG-NORMAL STOCHASTIC VOLATILITY MODEL WITH QUADRATIC DRIFT International Journal of Theoretical and Applied Finance Pub Date : 2024-02-28 ARTUR SEPP, PARVIZ RAKHMONOV
In this paper, we introduce the log-normal stochastic volatility (SV) model with a quadratic drift to allow arbitrage-free valuation of options on assets under money-market account and inverse martingale measures. We show that the proposed volatility process has a unique strong solution, despite non-Lipschitz quadratic drift, and we establish the corresponding Feynman–Kac partial differential equation
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PARAMETER ESTIMATION METHODS OF REQUIRED RATE OF RETURN ON STOCK International Journal of Theoretical and Applied Finance Pub Date : 2024-02-28 BATTULGA GANKHUU
In this study, we introduce new estimation methods for the required rate of returns on equity of private and public companies using the stochastic dividend discount model (DDM). To estimate the required rate of return on equity, we use the maximum likelihood method, the Bayesian method, and the Kalman filtering. We apply the model to a set of firms from the S&P 500 index using historical dividend and
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TAIL RISK MONOTONICITY IN GARCH(1,1) MODELS International Journal of Theoretical and Applied Finance Pub Date : 2024-02-27 PAUL GLASSERMAN, DAN PIRJOL, QI WU
The stationary distribution of a GARCH(1,1) process has a power law decay, under broadly applicable conditions. We study the change in the exponent of the tail decay under temporal aggregation of parameters, with the distribution of innovations held fixed. This comparison is motivated by the fact that GARCH models are often fit to the same time series at different frequencies. The resulting models
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PAIRS TRADING WITH TOPOLOGICAL DATA ANALYSIS International Journal of Theoretical and Applied Finance Pub Date : 2024-02-22 SOURAV MAJUMDAR, ARNAB KUMAR LAHA
In this paper, we propose a pairs trading strategy using the theory of topological data analysis (TDA). The proposed strategy is model-free. We propose a TDA-based distance to measure dependence between a pair of stochastic processes. We derive an upper bound of this distance in terms of a function of the canonical correlation of the processes, which allows for interpretability of this distance. We
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MULTIVARIATE HAWKES-BASED MODELS IN LIMIT ORDER BOOK: EUROPEAN AND SPREAD OPTION PRICING International Journal of Theoretical and Applied Finance Pub Date : 2024-02-19 QI GUO, ANATOLIY SWISHCHUK, BRUNO RÉMIlLARD
In this paper, we consider the pricing problem of European options and spread options for the Hawkes-based model in the limit order book (LOB). We introduce a variant of Hawkes process and consider its limit theorems, namely the exponential multivariate general compound Hawkes process (EMGCHP). We also consider a special case of one-dimensional EMGCHP and its limit theorems. Option pricing with one-dimensional
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OPTIMAL TIMES TO BUY AND SELL A HOME International Journal of Theoretical and Applied Finance Pub Date : 2024-02-19 MATTHEW LORIG, NATCHANON SUAYSOM
We consider a financial market in which the risk-free rate of interest is modeled as a Markov diffusion. We suppose that home prices are set by a representative homebuyer, who can afford to pay only a fixed cash flow per unit time for housing. The cash flow is a fraction of the representative homebuyer’s salary, which grows at a rate that is proportional to the risk-free rate of interest. As a result
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SYSTEMIC PERSPECTIVE OF TERM RISK IN BANK FUNDING MARKETS International Journal of Theoretical and Applied Finance Pub Date : 2024-02-15 ANDREA MACRINA, OBEID MAHOMED
The transition from term-based reference rates to overnight reference rates has created a dislocation in the market-making processes between the interbank and non-interbank funding, and their respective derivatives markets. This dislocation can be attributed to differences in funding and corresponding interest rate swap transactions, a thesis we explain and characterize in detail. It is then shown
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A GREEDY ALGORITHM FOR HABIT FORMATION UNDER MULTIPLICATIVE UTILITY International Journal of Theoretical and Applied Finance Pub Date : 2024-01-29 SNEZHANA KIRUSHEVA, THOMAS S. SALISBURY
In this paper, we consider the problem of optimizing lifetime consumption under a habit formation model, both with and without an exogenous pension. Unlike much of the existing literature, we apply a power utility to the ratio of consumption to habit, rather than to their difference. The martingale/duality method becomes intractable in this setting, so we develop a greedy version of this method that
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“IS DECARBONIZATION PRICED IN?”—EVIDENCE ON THE CARBON RISK HYPOTHESIS FROM THE EUROPEAN GREEN DEAL LEAKAGE SHOCK International Journal of Theoretical and Applied Finance Pub Date : 2023-11-27 LUKAS MUELLER, MARC RINGEL, DIRK SCHIERECK
On November 29, 2019, 12 days before its announcement, information on the ambitions of the European Green Deal was leaked. The leakage should have triggered a Europe-wide systemic shock to financial markets without an accompanying announcement of supportive measures. Applying event study methodology to a sample of 600 European large and mid-cap stocks, we find that the overall market reaction was indeed
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BEATING A CONSTANT WEIGHT BENCHMARK: EASIER DONE THAN SAID International Journal of Theoretical and Applied Finance Pub Date : 2023-08-01 PETER A. FORSYTH, PIETER M. VAN STADEN, YUYING LI
We determine a simple dynamic benchmark for asset allocation by solving an optimal stochastic control problem for outperforming the traditional constant proportion benchmark. An objective function based on a time averaged quadratic deviation from an elevated benchmark is proposed. We argue that this objective function combines the best features of tracking error and tracking difference. Assuming parametric
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MARKOVIAN STOCHASTIC VOLATILITY WITH STOCHASTIC CORRELATION — JOINT CALIBRATION AND CONSISTENCY OF SPX/VIX SHORT-MATURITY SMILES International Journal of Theoretical and Applied Finance Pub Date : 2023-07-27 MARTIN FORDE, BENJAMIN SMITH
In this paper, we show how to calibrate a general Markovian stochastic volatility model with stochastic correlation to the VIX implied volatility smile and the overall level, slope and curvature of the SPX smile in the T→0 limit. Explicit formulae are obtained for the asymptotic VIX smile for Heston and SABR-type models with mean reversion, and the Lewis CEV-p-model. We also discuss how the Bass martingale
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RATING TRANSITIONS FORECASTING: A FILTERING APPROACH International Journal of Theoretical and Applied Finance Pub Date : 2023-07-13 ARESKI COUSIN, JÉRǑME LELONG, TOM PICARD
Analyzing the effect of business cycle on rating transitions has been a subject of great interest these last 15 years, particularly due to the increasing pressure coming from regulators for stress testing. In this paper, we consider that the dynamics of rating migrations, in a pool of credit references, is governed by a common unobserved latent Markov chain. We explain how the current state of the
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CORRELATION ESTIMATION IN HYBRID SYSTEMS International Journal of Theoretical and Applied Finance Pub Date : 2023-07-12 Baron Law
A simple method is proposed to estimate the instantaneous correlations between state variables in a hybrid system from the empirical correlations between observable market quantities such as spot rates, stock prices and implied volatilities. The new algorithm is extremely fast since only low-dimension linear systems are involved. If the resulting matrix from the linear systems is not positive semidefinite
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THE FRACTIONAL VOLATILITY MODEL AND ROUGH VOLATILITY International Journal of Theoretical and Applied Finance Pub Date : 2023-07-08 R. VILELA MENDES
The question of the volatility roughness is interpreted in the framework of a data-reconstructed fractional volatility model, where volatility is driven by fractional noise. Some examples are worked out and, using the Malliavin calculus for fractional processes, an option pricing equation and its solution are obtained.
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CORRELATION MATRIX OF EQUI-CORRELATED NORMAL POPULATION: FLUCTUATION OF THE LARGEST EIGENVALUE, SCALING OF THE BULK EIGENVALUES, AND STOCK MARKET International Journal of Theoretical and Applied Finance Pub Date : 2023-04-19 YOHJI AKAMA
Given an N-dimensional sample of size T, form a sample correlation matrix C. Suppose that N and T tend to infinity with T/N converging to a fixed finite constant Q>0. If the population is a factor model, then the eigenvalue distribution of C almost surely converges weakly to Marčenko–Pastur distribution such that the index is Q and the scale parameter is the limiting ratio of the specific variance
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APPROXIMATING OPTION PRICES UNDER LARGE CHANGES OF UNDERLYING ASSET PRICES International Journal of Theoretical and Applied Finance Pub Date : 2023-04-17 JAE-YUN JUN, YVES RAKOTONDRATSIMBA
When one invests in portfolios of derivatives (such as options), the delta-gamma approximation (DGA) is often used as a risk management strategy to reduce the risk associated with the underlying asset price. However, this approximation is locally accepted only for small changes of the underlying asset price. When these changes become large, the option prices estimated by the DGA may significantly differ
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SUBLEADING CORRECTION TO THE ASIAN OPTIONS VOLATILITY IN THE BLACK–SCHOLES MODEL International Journal of Theoretical and Applied Finance Pub Date : 2023-03-23 DAN PIRJOL
The short maturity limit T→0 for the implied volatility of an Asian option in the Black–Scholes model is determined by the large deviations property for the time-average of the geometric Brownian motion. In this note, we derive the subleading O(T) correction to this implied volatility, using an asymptotic expansion for the Hartman–Watson distribution. The result is used to compute subleading corrections
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DOLLAR COST AVERAGING RETURNS ESTIMATION International Journal of Theoretical and Applied Finance Pub Date : 2023-03-10 HAYDEN BROWN
Given a geometric Brownian motion wealth process, a log-Normal lower bound is constructed for the returns of a regular investing schedule. The distribution parameters of this bound are computed recursively. For dollar cost averaging (equal amounts in equal time intervals), parameters are computed in closed form. A lump sum (single amount at time 0) investing schedule is described which achieves a terminal
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BOUNDED STRATEGIES FOR MAXIMIZING THE SHARPE RATIO International Journal of Theoretical and Applied Finance Pub Date : 2023-02-27 JIANG YE, YIWEI WANG, MUHAMMAD WAJID RAZA
Bernard et al. [(2019) Optimal strategies under omega ratio, European Journal of Operational Research 275 (2), 755–767] use convex ordering arguments to determine the bounded payoff for maximizing the omega ratio. However, it appears difficult to apply such reasoning to estimate the bounded payoff for maximizing the Sharpe ratio. As a proposed solution, this paper uses a Lagrange multiplier method
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KELLY TRADING AND MARKET EQUILIBRIUM International Journal of Theoretical and Applied Finance Pub Date : 2023-01-31 HANS-PETER BERMIN, MAGNUS HOLM
The Kelly framework is the natural multi-period extension of the one-period mean-variance model of Markowitz in the sense that the efficient frontier is characterized by trading strategies having maximal instantaneous Sharpe ratio. We show that Kelly traders naturally trade in such a way as to induce an equilibrium for the instantaneous covariance matrix. This equilibrium, arising from trading alone
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VOLATILITY SMILE INTERPOLATION WITH RADIAL BASIS FUNCTIONS International Journal of Theoretical and Applied Finance Pub Date : 2023-01-21 HERMANN AZEMTSA DONFACK, CELESTIN WAFO SOH, ANTONIE KOTZE
The Radial Basis Functions (RBF) interpolation is a popular approximation technique used to smooth scattered data in various dimensions. This study uses RBF interpolation to interpolate the volatility skew of the S&P500 index options. The interpolated skews are used to construct the risk-neutral densities of the index and its local volatility surface. The RBF interpolation is contrasted throughout
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WEAK ERROR RATES FOR OPTION PRICING UNDER LINEAR ROUGH VOLATILITY International Journal of Theoretical and Applied Finance Pub Date : 2023-01-19 CHRISTIAN BAYER, ERIC JOSEPH HALL, RAÚL TEMPONE
In quantitative finance, modeling the volatility structure of underlying assets is vital to pricing options. Rough stochastic volatility models, such as the rough Bergomi model [C. Bayer, P. K. Friz & J. Gatheral (2016) Pricing under rough volatility, Quantitative Finance 16 (6), 887–904, doi:10.1080/14697688.2015.1099717], seek to fit observed market data based on the observation that the log-realized
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OPTIMAL INVESTMENT IN INTERRELATED PROJECTS International Journal of Theoretical and Applied Finance Pub Date : 2023-01-13 SHASIKANTA NAINDEBAM, MARZIA RAYBAUDI, MARTIN SOLA
This paper addresses the effects in partial equilibrium models of relaxing one of the critical underlying assumptions of [A. K. Dixit & R. S. Pindyck (1994) Investment Under Uncertainty. Princeton: Princeton University Press] to investment under uncertainty: either the potential investor has access to a single project or can consider competing (or complementary) projects independently. This paper studies
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ACCOUNTING NOISE AND THE PRICING OF CoCos International Journal of Theoretical and Applied Finance Pub Date : 2022-12-13 MIKE DERKSEN, PETER SPREIJ, SWEDER VAN WIJNBERGEN
Contingent Convertible bonds (CoCos) convert into equity or are written down in times of distress. Existing pricing models assume conversion triggers based on market prices assuming that markets observe all relevant information. We incorporate that markets receive information through noisy accounting reports only, distinguish between market and accounting values and incorporate that coupon payments
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SENSITIVITIES AND HEDGING OF THE COLLATERAL CHOICE OPTION International Journal of Theoretical and Applied Finance Pub Date : 2022-10-13 GRISELDA DEELSTRA, LECH A. GRZELAK, FELIX L. WOLF
The collateral choice option allows a collateral-posting party the opportunity to change the type of security in which the collateral is deposited. Due to nonzero collateral basis spreads, this optionality significantly impacts asset valuation. Because of the complexity of valuing the option, many practitioners resort to deterministic assumptions on the collateral rates. In this paper, we focus on
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A PRACTICAL ALGORITHM TO DETECT SUPEREXPONENTIAL BEHAVIOR IN FINANCIAL ASSET PRICE RETURNS International Journal of Theoretical and Applied Finance Pub Date : 2022-09-26 CHRISTOPHER LYNCH, BENJAMIN MESTEL
To assist with the detection of bubbles and negative bubbles in financial markets, a criterion is introduced to indicate whether a market is likely to be in a superexponential regime (where growth in such a regime would correspond to an asset price bubble and decline to an negative bubble) as opposed to “normal” exponential behavior typified by a constant rate of growth or decline. The criterion is
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OPTION SURFACE STATISTICS WITH APPLICATIONS International Journal of Theoretical and Applied Finance Pub Date : 2022-08-31 DILIP B. MADAN, KING WANG
At each maturity a discrete return distribution is inferred from option prices. Option pricing models imply a comparable theoretical distribution. As both the transformed data and the option pricing model deliver points on a simplex, the data is statistically modeled by a Dirichlet distribution with expected values given by the option pricing model. The resulting setup allows for maximum likelihood
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OPTIMAL PORTFOLIO CHOICE WITH CRASH AND DEFAULT RISK International Journal of Theoretical and Applied Finance Pub Date : 2022-08-24 LUKAS MÜLLER
We consider the worst-case scenario portfolio approach, introduced by Korn & Wilmott (2002), in a multi-asset setting, where asset defaults can occur in addition to asset crashes. In our model, the strictly risk-averse investor does not know which asset is affected by the worst-case scenario. Based on a reformulation of the value function we define the set of minimum constant portfolio processes. We
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A STOCHASTIC CONTROL APPROACH TO BID-ASK PRICE MODELLING International Journal of Theoretical and Applied Finance Pub Date : 2022-08-13 ENGEL JOHN C. DELA VEGA, ROBERT J. ELLIOTT
This paper develops a model for the bid and ask prices of a European-type asset by formulating a stochastic control problem. The state process is governed by a modified geometric Brownian motion whose drift and diffusion coefficients depend on a Markov chain. A Girsanov theorem for Markov chains is implemented for the change of coefficients, including the diffusion coefficient which cannot be changed
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VALUATION OF GENERAL CONTINGENT CLAIMS WITH SHORT SELLING BANS: AN EQUAL-RISK PRICING APPROACH International Journal of Theoretical and Applied Finance Pub Date : 2022-08-13 GUIYUAN MA, SONG-PING ZHU, IVAN GUO
This paper studies the valuation of general contingent claims with short selling bans under the equal-risk pricing (ERP) framework proposed in I. Guo & S.-P. Zhu (2017) [Journal of Economic Dynamics and Control 76, 136–151]. In existing literature, analytical pricing formulae were derived in the special case, where the payoff function is monotonic under risk-neutral measures. In this paper, we establish
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MULTIVARIATE DYNAMIC CASH SUB-ADDITIVE RISK MEASURES FOR PROCESSES International Journal of Theoretical and Applied Finance Pub Date : 2022-07-26 FEI SUN, KUI LUO, YU FENG
In this paper, we study a new class of dynamic risk measures for processes. These new risk measures are derived for the portfolio vectors and adapted to a given filtration. By introducing the notion of discount factor, we deeply analyze the property of cash sub-additivity for these risk measures. Furthermore, by expanding the risk position space, we derive the relationship between these new risk measures
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MARKET TIMING IN PARAMETRIC PORTFOLIO POLICIES International Journal of Theoretical and Applied Finance Pub Date : 2022-07-16 CARLOS OSORIO, THORSTEN PODDIG, CHRISTIAN FIEBERG, MICHAEL OLSCHEWSKY, MICHAEL FALGE
We extend the parametric portfolio policies that exploit firm characteristics to optimize portfolios of stocks and are thus based on asset selection. In addition to this, our extension exploits market indicators for market timing purposes (i.e. optimal allocations between stocks and a risk-free asset). We demonstrate the mechanics of the proposed technique in simulation studies. Specifically, we show
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PORTFOLIO VOLATILITY SPILLOVER International Journal of Theoretical and Applied Finance Pub Date : 2022-07-16 GUEORGUI S. KONSTANTINOV, FRANK J. FABOZZI
In this paper, the authors estimate portfolio volatilities and use variance−decomposition techniques and Cholesky factorization to construct a portfolio volatility spillover index. Furthermore, the authors show that spillover risks are persistent and much more common than well-known indicators like the turbulence index and the CBOE VIX index might suggest. Moreover, portfolio volatilities show contributions
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OPTIMAL INVESTMENT AND CONTINGENT CLAIM VALUATION WITH EXPONENTIAL DISUTILITY UNDER PROPORTIONAL TRANSACTION COSTS International Journal of Theoretical and Applied Finance Pub Date : 2022-07-12 ALET ROUX, ZHIKANG XU
We consider indifference pricing of contingent claims consisting of payment flows in a discrete-time model with proportional transaction costs and under exponential disutility. This setting covers utility maximization of terminal wealth as a special case. A dual representation is obtained for the associated disutility minimization problem, together with a dynamic procedure for solving it. This leads
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PRICING AND HEDGING PREPAYMENT RISK IN A MORTGAGE PORTFOLIO International Journal of Theoretical and Applied Finance Pub Date : 2022-07-07 EMANUELE CASAMASSIMA, LECH A. GRZELAK, FRANK A. MULDER, CORNELIS W. OOSTERLEE
Understanding mortgage prepayment is crucial for any financial institution providing mortgages, and it is important for hedging the risk resulting from such unexpected cash flows. Here, in the setting of a Dutch mortgage provider, we propose to include nonlinear financial instruments in the hedge portfolio when dealing with mortgages with the option to prepay part of the notional early. Based on the
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MARTINGALE REPRESENTATIONS IN PROGRESSIVE ENLARGEMENT BY MULTIVARIATE POINT PROCESSES International Journal of Theoretical and Applied Finance Pub Date : 2022-06-11 ANTONELLA CALZOLARI, BARBARA TORTI
In this paper, we show that all local martingales with respect to the initially enlarged natural filtration of a vector of multivariate point processes can be weakly represented up to the minimum among the explosion times of the components. We also prove that a strong representation holds if any multivariate point process of the vector has almost surely infinite explosion time and discrete marks space
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DIVIDENDS AND COMPOUND POISSON PROCESSES: A NEW STOCHASTIC STOCK PRICE MODEL International Journal of Theoretical and Applied Finance Pub Date : 2022-05-30 BATTULGA GANKHUU, JACOB KLEINOW, ALTANGEREL LKHAMSUREN, ANDREAS HORSCH
This study introduces a stochastic multi-period dividend discount model (DDM) that includes (i) a compound nonhomogenous Poisson process for dividend growth and (ii) the probability of firm default. We obtain maximum likelihood (ML) estimators and confidence interval formulas of our model parameters. We apply the model to a set of firms from the S&P 500 index using historical dividend and price data
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APPLYING THE LOCAL MARTINGALE THEORY OF BUBBLES TO CRYPTOCURRENCIES International Journal of Theoretical and Applied Finance Pub Date : 2022-04-08 SOON HYEOK CHOI, ROBERT A. JARROW
Cryptocurrencies provide a natural setting to test for the existence of price bubbles using the local martingale theory of bubbles because cryptocurrencies have no cash flows. Using a robust statistical algorithm, we test for price bubbles in eight cryptocurrencies, Bitcoin (BTC), Litecoin (LTC), Ethereum (ETH), Ripple (XRP), Bitcoin Cash (BCH), EOS (EOS), Monero (XMR), and Zcash (ZEC), from 1 January
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OPTIMAL CROSS-CURRENCY MORTGAGE DECISIONS International Journal of Theoretical and Applied Finance Pub Date : 2022-03-21 EVA LÜTKEBOHMERT, THORSTEN SCHMIDT, TIANJIAO ZHU
In this paper, we study optimal mortgage decisions in a cross-currency setting. In particular, we address the question on how a household should optimally split its mortgage portfolio in a fixed rate mortgage in the domestic currency and an adjustable rate mortgage denominated in a foreign currency subject to some risk constraints. We propose an affine factor model which allows to jointly investigate
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AN EMPIRICAL ANALYSIS OF OPTION PRICING WITH SHORT SELL BANS International Journal of Theoretical and Applied Finance Pub Date : 2022-03-19 MESIAS ALFEUS, XIN-JIANG HE, SONG-PING ZHU
Short sell bans are often imposed during a financial crisis as a desperate measure to stabilize financial markets. Yet, the impact of short sell bans on option pricing and hedging is not well studied, at least quantitatively, until very recently when Guo & Zhu [(2017) Equal risk pricing under convex trading constraints, Journal of Economic Dynamics and Control 76, 136–151] and He & Zhu [(2020) A revised
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CALIBRATING LOCAL VOLATILITY MODELS WITH STOCHASTIC DRIFT AND DIFFUSION International Journal of Theoretical and Applied Finance Pub Date : 2022-03-18 ORCAN ÖGETBIL, NARAYAN GANESAN, BERNHARD HIENTZSCH
We propose Monte Carlo calibration algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates and finally stochastic local volatility with stochastic interest rates. For each model, we include detailed derivations of the corresponding SDE systems and list the required input data and steps for calibration. We give conditions
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APPROXIMATE OPTION PRICING FORMULA FOR BARNDORFF-NIELSEN AND SHEPHARD MODEL International Journal of Theoretical and Applied Finance Pub Date : 2022-03-15 TAKUJI ARAI
For the Barndorf-Nielsen and Shephard model, we present approximate expressions of call option prices based on the decomposition formula developed by [T. Arai (2021) Alos type decomposition formula for Barndor-Nielsen and Shephard model, Journal of Stochastic Analysis 2 (2), 3]. Besides, some numerical experiments are also implemented to make sure how effective our approximations are.
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A STOCHASTIC OIL PRICE MODEL FOR OPTIMAL HEDGING AND RISK MANAGEMENT International Journal of Theoretical and Applied Finance Pub Date : 2022-03-15 TEEMU PENNANEN, LUCIANE SBARAINI BONATTO
In this paper, we develop a stochastic model for future monthly spot prices of the most important crude oils and refined products. The model is easy to calibrate to both historical data and views of a user even in the presence of negative prices which have been observed recently. This makes it particularly useful for risk management and design of optimal hedging strategies in incomplete market situations
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A MEAN-FIELD EXTENSION OF THE LIBOR MARKET MODEL International Journal of Theoretical and Applied Finance Pub Date : 2022-03-05 SASCHA DESMETTRE, SIMON HOCHGERNER, SANELA OMEROVIC, STEFAN THONHAUSER
In this paper, we introduce a mean-field extension of the LIBOR market model (LMM) which preserves the basic features of the original model. Among others, these features are the martingale property, a directly implementable calibration and an economically reasonable parametrization of the classical LMM. At the same time, the mean-field LIBOR market model (MF-LMM) is designed to reduce the probability
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DYNAMIC UTILITY AND RELATED NONLINEAR SPDES DRIVEN BY LÉVY NOISE International Journal of Theoretical and Applied Finance Pub Date : 2022-02-28 ANIS MATOUSSI, MOHAMED MRAD
In this work, we study a class of consistent dynamic utilities in a incomplete financial market including jumps. First, we show that the dynamic utility is solution of a non-linear second-order stochastic partial integro-differential equation (SPIDE). Second, a complete study of the primal and the dual problems, allows us, firstly, to establish a connection between the utility-SPIDE and two SDEs satisfied
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SHORT SELLING WITH MARGIN RISK AND RECALL RISK International Journal of Theoretical and Applied Finance Pub Date : 2022-02-28 KRISTOFFER GLOVER, HARDY HULLEY
To investigate the effect of short-selling constraints on investor behavior, we formulate an optimal stopping model in which the decision to cover a short position is affected by two short sale-specific frictions — margin risk and recall risk. Margin risk is introduced by assuming that a short seller is forced to close out their position involuntarily if they cannot fund margin calls (since short sales
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TRADING MULTIPLE MEAN REVERSION International Journal of Theoretical and Applied Finance Pub Date : 2022-02-23 ELENA BOGUSLAVSKAYA, MICHAEL BOGUSLAVSKY, DMITRY MURAVEY
How should one construct a portfolio from multiple mean-reverting assets? Should one add an asset to a portfolio even if the asset has zero mean reversion? We consider a position management problem for an agent trading multiple mean-reverting assets. We solve an optimal control problem for an agent with power utility, and present an explicit solution for several important special cases and a semi-explicit
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SOLVENCY MEASUREMENT OF LIFE ANNUITY PRODUCTS International Journal of Theoretical and Applied Finance Pub Date : 2022-02-21 PAULINE NGUGNIE DIFFOUO, PIERRE DEVOLDER
In this paper, we measure the market and the longevity risks borne by an insurer by computing their solvency capital for a given annuity and within an investment strategy. For this purpose, we propose the investment strategy in such a way as to mitigate the solvency capital of the insurer and improve the internal rate of return of a shareholder investing on a given annuity. Numerically, we study the
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LARGE PLATONIC MARKETS WITH DELAYS International Journal of Theoretical and Applied Finance Pub Date : 2022-02-19 YANNICK LIMMER, THILO MEYER-BRANDIS
The objective is to develop a general stochastic approach to delays on financial markets. We suggest such a concept in the context of large Platonic markets, which allow infinitely many assets and incorporate a restricted information setting. The discussion is divided into information delays and order execution delays. The former enables modeling of markets, where the observed information is delayed
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OPTIMAL PORTFOLIO CHOICE WITH CRASH RISK AND MODEL AMBIGUITY International Journal of Theoretical and Applied Finance Pub Date : 2022-02-09 RALF KORN, LUKAS MÜLLER
In this paper, we consider a continuous time portfolio optimization problem that includes the possibility of a crash scenario as well as parameter uncertainty. To do this, we combine the worst-case scenario approach, introduced by Korn & Wilmott (2002) with a model ambiguity approach that is also based on Knightian uncertainty. In our model, the crash scenario occurs at the worst possible time for
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HEDGING OF AMERICAN OPTIONS IN ILLIQUID MARKETS WITH PRICE IMPACTS International Journal of Theoretical and Applied Finance Pub Date : 2022-01-20 ALEXANDRE F. ROCH
We consider a setup in which a large trader has sold a number of American-style derivatives and can have an impact on prices by trading the underlying asset for hedging purposes. The price impacts are assumed to be temporary and decay exponentially with time. Due to the impact of trading on prices, the large trader may also be tempted to minimize the payoff of the derivative by manipulating the underlying
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INFLATION, CENTRAL BANK AND SHORT-TERM INTEREST RATES: A NEW MODEL WITH CALIBRATION TO MARKET DATA International Journal of Theoretical and Applied Finance Pub Date : 2022-01-12 FLAVIA ANTONACCI, CRISTINA COSTANTINI, FERNANDA D’IPPOLITI, MARCO PAPI
In this paper, we propose a new model for the joint evolution of the inflation rate, the Central Bank official interest rate and the short-term interest rate. Our model takes into account the fact that the Central Bank interest rate changes at random times, inflation is measured at fixed, regular times, while the short-term interest rate evolves essentially continuously. We derive the valuation equation
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SINH-ACCELERATION FOR B-SPLINE PROJECTION WITH OPTION PRICING APPLICATIONS International Journal of Theoretical and Applied Finance Pub Date : 2022-01-07 SVETLANA BOYARCHENKO, SERGEI LEVENDORSKIĬ, J. LARS KYRKBY, ZHENYU CUI
We clarify the relations among different Fourier-based approaches to option pricing, and improve the B-spline probability density projection method using the sinh-acceleration technique. This allows us to efficiently separate the control of different sources of errors better than the FFT-based realization allows; in many cases, the CPU time decreases as well. We demonstrate the improvement of the B-spline
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PRICING ASIAN OPTIONS WITH CORRELATORS International Journal of Theoretical and Applied Finance Pub Date : 2021-12-30 SILVIA LAVAGNINI
We derive a series expansion by Hermite polynomials for the price of an arithmetic Asian option. This requires the computation of moments and correlators of the underlying asset price which for a polynomial jump–diffusion process are given analytically; hence, no numerical simulation is required to evaluate the series. This allows to derive analytical expressions for the option Greeks. The weight function
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COHERENT RISK MEASURE ON L0: NA CONDITION, PRICING AND DUAL REPRESENTATION International Journal of Theoretical and Applied Finance Pub Date : 2021-12-29 EMMANUEL LEPINETTE, DUC THINH VU
The NA condition is one of the pillars supporting the classical theory of financial mathematics. We revisit this condition for financial market models where a dynamic risk-measure defined on L0 is fixed to characterize the family of acceptable wealths that play the role of nonnegative financial positions. We provide in this setting a new version of the fundamental theorem of asset pricing and we deduce
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THE VIX AND FUTURE INFORMATION International Journal of Theoretical and Applied Finance Pub Date : 2021-12-29 MARKUS HESS
In this paper, we propose an innovative VIX model which takes future market information available to the traders into account. The future information is modeled by an initially enlarged filtration in our setup. We derive an explicit representation for the anticipative VIX process and obtain the associated time dynamics. We also investigate the pricing of variance swaps under both backward- and forward-looking
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MODELING LIFETIME EXPECTED CREDIT LOSSES ON BANK LOANS International Journal of Theoretical and Applied Finance Pub Date : 2021-12-09 THAMAYANTHI CHELLATHURAI
The guidelines of various Accounting Standards require every financial institution to measure lifetime expected credit losses (LECLs) on every instrument, and to determine at each reporting date if there has been a significant increase in credit risk since its inception. This paper models LECLs on bank loans given to a firm that has promised to repay debt at multiple points over the lifetime of the
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PORTFOLIO INSURANCE UNDER ROUGH VOLATILITY AND VOLTERRA PROCESSES International Journal of Theoretical and Applied Finance Pub Date : 2021-11-24 JEAN-LOUP DUPRET, DONATIEN HAINAUT
Affine Volterra processes have gained more and more interest in recent years. In particular, this class of processes generalizes the classical Heston model and the more recent rough Heston model. The aim of this work is hence to revisit and generalize the constant proportion portfolio insurance (CPPI) under affine Volterra processes. Indeed, existing simulation-based methods for CPPI do not apply easily