RANDOM TIME FORWARD-STARTING OPTIONS

We introduce a natural generalization of the forward-starting options. The main feature of the contract presented here is that the strike-determination time is not fixed ex-ante, but allowed to be random, usually related to the occurrence of some event, either of financial nature or not. We will call these options random time forward-starting (RTFS). We show that, under an appropriate “martingale preserving” hypothesis, we can exhibit arbitrage free prices, which can be explicitly computed in many classical market models, at least under independence and in absence of simultaneous jumps between the random time and the assets’ prices. Practical implementations of the pricing methodologies are also provided. Finally, a credit value adjustment (CVA) formula for these over the counter (OTC) options is computed for the unilateral counterparty credit risk.