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- Title
Performance of Two Numerical Methods in Option Price Calculation.
- Authors
Emy Siswanah; Minhayati Saleh; Emamatul Qudsiyah; Muhammad Malik Hakim
- Abstract
This study employed two different numerical methods in calculating American option prices. Implied volatility was calculated using the Newton-Raphson method, while American option pricing was determined using the Monte Carlo method. American options necessitate a numerical solution to parabolic differential equations; thus, this decision is made by pursuing such a solution. A numerical solution is also necessary for the volatility value calculated from the market's implications for option prices. The Nasdaq share market served as the source of information in this study. This research examined the effectiveness of the Monte Carlo method coupled with Newton-Raphson implied volatility in American option pricing across three case studies. According to the findings, the Newton-Raphson method possessed a small error and a fast convergence rate for estimating volatility. However, the Monte Carlo option pricing was preferable to other methods since it resulted in a smaller MAPE value. The MAPE value calculated using the Monte Carlo method with Newton-Raphson implied volatility was lower than that calculated using the Monte Carlo method with historical volatility. The American option pricing generated by the Monte Carlo method with Newton-Raphson implied volatility was more in line with market option prices. The Newton-Raphson method yielded volatility values that shifted in response to market conditions. Because of this fluctuation in the volatility values, the Newton-Raphson method lent its support to the Monte Carlo method for estimating American option prices. Newton-Raphson and Monte Carlo have become two popular numerical methods for option pricing, and both delivered satisfactory results.
- Subjects
NASDAQ Stock Market; PRICES; NUMERICAL solutions to differential equations; NEWTON-Raphson method; VALUE (Economics); MARKET prices
- Publication
Engineering Letters, 2024, Vol 32, Issue 3, p541
- ISSN
1816-093X
- Publication type
Article