In the present work, a two-dimensional Haar wavelet method is proposed to study the sensitivities of the price of an option. The method is appropriate to study these sensitivities as it explicitly gives the values of all the derivatives of the solution. A Black–Scholes model for European style options is considered to analyze the physical and numerical aspects of the put and the call option Greeks. We use the concept of coordinate transformation to make the Black–Scholes equation dimensionless and to resolve the obstacle in approximating the Greeks having non-smoothness at the strike price. The infinite spatial domain is truncated into the finite domain to avoid large truncation errors. Through rigorous analysis, the method is shown first-order accurate in the L²−norm. The numerical computations performed to approximate the option price and various Greeks, like delta, theta, gamma, and so forth, confirm the theoretical results in L²−norm. The relative errors and the maximum absolute errors are also presented. The motivational work of option Greeks analysis may leave a significant impact on financial institutes; it helps them to manage the risk by setting the portfolio's new value and to estimate the probability of losing money.

中文翻译：

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基于二维 Haar 小波的近似技术研究期权价格的敏感性

在目前的工作中，提出了一种二维 Haar 小波方法来研究期权价格的敏感性。该方法适用于研究这些敏感性，因为它明确给出了解决方案的所有导数的值。欧式期权的 Black-Scholes 模型被考虑用于分析希腊看跌期权和看涨期权的物理和数字方面。我们使用坐标变换的概念来使 Black-Scholes 方程无量纲，并解决在执行价格处逼近具有非平滑性的希腊人的障碍。无限空间域被截断为有限域以避免大的截断误差。通过严格的分析，该方法在L ²中表现出一阶精度-规范。为近似期权价格和各种希腊字母（如 delta、theta、gamma 等）执行的数值计算证实了L ² -norm 中的理论结果。还给出了相对误差和最大绝对误差。期权希腊人分析的激励工作可能会对金融机构产生重大影响；它通过设置投资组合的新价值和估计亏损的可能性来帮助他们管理风险。