Abstract
We consider a risk-neutral stock-price model where the volatility and the return processes are assumed to be dependent. The market is complete and arbitrage-free. Using a linear regression approach, explicit functions of risk-neutral density functions of stock return functions are obtained and closed form solutions of the corresponding Black-Scholes-type option pricing results are derived. Implied volatility skewness properties are illustrated.
Highlights
Stochastic volatility (SV) modeling is the subject of several papers in the option price literature
It is known that under a Black-Scholes model formulation the implied volatility function must remain constant for different values of the strike price when the other parameters of the option pricing model are kept constant
We find a suitable value for implied volatility σ ∗ so that call option price values both under
Summary
Stochastic volatility (SV) modeling is the subject of several papers in the option price literature. In [2], one has to numerically integrate conditional characteristic functions obtained as solutions of nonlinear pdf to derive the call option prices. (2016) A Linear Regression Approach for Determining Explicit Expressions for Option Prices for Equity Option Pricing Models with Dependent Volatility and Return Processes. R. Jagannathan in the paper [5], which obtains Call Option Price Conditional on the variance rate V 2 and derives the unconditional call price by integrating using an approximate probability density function g (V ). The proposed two-factor stock price model that allows the volatility factor and the Brownian motion return processes to be dependent and a linear regression approach that derives explicit expressions for the distribution functions of log return of a stock or stock index are used. We provide concluding remarks and suggestions for future direction
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