PRICING OPTIONS FROM THE POINT OF VIEW OF A TRADER

This paper is a contribution to the pricing and hedging of options in a market where the volatility is stochastic. The new concept of relative indifference pricing is further developed. This relative price is the price at which an option trader is indifferent to trade in an additional option, given that he is currently holding and dynamically hedging a portfolio of options. We find that the appropriate volatility risk premium depends on the trader's risk aversion coefficient and his portfolio position before selling or buying the additional option. We suggest two asymptotic expansions which relate the volatility risk premium to the Vega of the option portfolio. This approach provides a tool for traders to (i) integrate option pricing with risk management and (ii) quote competitive prices that depend on their aggregate risk exposure.