The Optimal Rehedging Interval for the Options Portfolio within the RAPM, Taking into Account Transaction Costs and Liquidity Costs

Abstract

Using the approach of L.C.G. Rogers and S. Singh, we added liquidity costs accounting to the model with risk adjusted pricing methodology (RAPM), generalized by M. Jandacka and D. Sevcovic. This model minimizes the risk of transaction costs growth from the frequent delta hedging, and reduces the risk of the portfolio value changes (hedging error) due to rare rebalances. Numerical solution for price of option combination ”short strangle” is found. An optimal interval of time for delta hedging is considered. Corresponding results are presented in the form of graphs characterizing the dependence of the interval on the current price of the underlying asset and on the time remaining until the expiration of options.

Keywords

• rehedging interval
• non-linear option pricing model
• rapm
• transaction costs
• liquidity cost
• delta hedging