Pricing options on trading strategies

Option pricing and dynamic trading strategies are two fundamental topics in financial mathematics. This thesis investigates the interrelation between these two topics. To insure against adverse outcomes from dynamic strategies, new derivatives have arisen or are needed, whose payoff depends on the profit and loss of the strategies. We choose to study the pricing of options on the P&L obtained following two classes of trading strategies: (1) options on optimal strategies and (2) options on leverage strategies. We consider that both classes of strategies are invested in a risky asset whose price follows a geometric Brownian motion with stochastic volatility. Our pricing scheme assumes that the volatility evolves independently of the trading asset, but requires no other modelling of the volatility dynamics. As a result, this scheme has minimal modelling risks associated with volatility.;In Chapter 2, we study strategy options. These are call options on the nal P&L obtained following an optimal strategy, optimizing over a class of trading strategies whose position in the risky asset is subject to constraints. After identifying the optimal strategy, we then price the strategy options relative to co-terminal European calls on the trading asset. Strategy options are a generalization of passport options. This study builds on prior work about passport options, along with work about lookback options.;In Chapter 3, we introduce and study options on CPPI. These are options on the P&L obtained using leverage strategies originating from Constant Proportion Portfolio Insurance (CPPI). The options considered vary in their payoff and in the structure of the leverage. Except for one case, we price these options relative to the co-terminal European claims on the trading asset. For the remaining case, we compute the price as an explicit function of the asset price.;In the Appendix, we revisit two problems concerning CPPI. First, we prove that CPPI is an optimal strategy for maximizing a HARA utility function. Second, we study the optimal execution of CPPI in the presence of transaction costs.