This paper presents a model for the market making of options on a liquid stock. The stock price follows a generic stochastic volatility model under the real-world probability measure P. Market participants price options on this stock under a riskneutral pricing measure Q, and they may misspecify the parameters controlling the dynamics of the volatility process. We¯rst consider that there is a risk-neutral agent who is willing to make markets in an option on the stock, with the aim of maximizing the expected terminal wealth at maturity. Using standard tools in optimal stochastic control, we provide analytical expressions for the optimal bid and ask quotes of the market maker. We then assume that the agent is risk-averse, and perturb the linear utility function by adding a variance term. In this setting, analytic approximations of the optimal bid and ask quotes are obtained. In the case where the stock price process follows a Heston model, Monte Carlo simulations are used to compare the optimal strategy to a \zero-intelligence" strategy, and to highlight the e®ects of some parameters misspeci¯cation on the performance of the strategy.

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Abstract. The question addressed in this paper is the performance of the optimal strategy, and the impact of partial information. The setting we consider is that of a stochastic asset price model where the trend follows an unobservable Ornstein-Uhlenbeck process. We focus on the optimal strategy with a logarithmic utility function under full or partial information. For both cases, we provide the asymptotic expectation and variance of the logarithmic return as functions of the signal-to-noise ratio and of the trend mean reversion speed. Finally, we compare the asymptotic Sharpe ratios of these strategies in order to quantify the loss of performance due to partial information.

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