Derivation of a Pricing Model for European Calls with Transaction Costs under the Heston Stochastic Volatility
Joy Ijeoma Adindu-Dick *
Department of Mathematics, Imo State University, Owerri, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
An option as a financial security, gives the holder the right to buy or sell an underlying asset at a predetermined price on a specified date. Option pricing which plays a vital role in financial market deals with valuing the price of an option using variables like stock price, interest rate, exercise price, expiration time, volatility. This work deals with the derivation of the pricing Partial Differential Equations (PDEs) for European calls with transaction costs under the Heston stochastic volatility. The Heston stochastic volatility is chosen because it follows a process that is more adaptable to the market which is the mean reverting process. We obtain our formulation by utilizing a familiar option without transaction costs in its price and using a dynamic hedging strategy. Our final pricing PDE does not include the familiar option and it reduces to the original Heston PDE when transaction costs are eliminated.
Keywords: European calls, transaction costs, heston stochastic volatility, dynamic hedging strategy, options pricing