Financial Derivatives Pricing under Stochastic Alpha Beta Rho(SABR) Model
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초록
There are many approaches to treat volatilities. Among them, we adopt a stochastic volatility model, especially, the Stochastic Alpha Beta Rho (SABR) model. In this work we have two directions: to evaluate option prices, and to provide volatility properties. For the option pricing we have two steps: parameter calibration for SABR model and option pricing based on the calibration. We adopt the KOSPI200 option’s implied volatility to calibrate SABR parameters for the market data. Based on the calibration, we try to compute the option prices. To evaluate the prices, there are two well-known methodologies: Monte Carlo simulation and finite difference method (FDM). We figure out fair value of European option, Barrier option, and Equity Linked Securities (ELS) under SABR model using both methods. Furthermore, we draw the loss probability density functions of ELS for each used models. By using the parameters obtained by calibration and the implied volatility formula under the SABR model, we provide several quantitative properties of volatility by drawing volatility skew, term structure and surface.
Abstract
There are many approaches to treat volatilities. Among them, we adopt a stochastic volatility model, especially, the Stochastic Alpha Beta Rho (SABR) model. In this work we have two directions: to evaluate option prices, and to provide volatility properties. For the option pricing we have two steps: parameter calibration for SABR model and option pricing based on the calibration. We adopt the KOSPI200 option’s implied volatility to calibrate SABR parameters for the market data. Based on the calibration, we try to compute the option prices. To evaluate the prices, there are two well-known methodologies: Monte Carlo simulation and finite difference method (FDM). We figure out fair value of European option, Barrier option, and Equity Linked Securities (ELS) under SABR model using both methods. Furthermore, we draw the loss probability density functions of ELS for each used models. By using the parameters obtained by calibration and the implied volatility formula under the SABR model, we provide several quantitative properties of volatility by drawing volatility skew, term structure and surface.
참고문헌 (7)
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- West, G., "Calibration of the SABR Model in Illiquid Markets", Applied Mathematical Finance, 12(4), pp.371~385 (2005)