The Russian Option: Reduced Regret

The Russian Option: Reduced Regret

We propose a new put asset where the option buyer receives the maximum price (discounted) that the option has ever traded at during the time period (which may be inde nitely long) between the purchase time and the exercise time | so that the buyer need look at the uctuations only occasionally and enjoys having little or no regret that he didn't exercise the option at an earlier time (except for...

The British Russian Option

Following the economic rationale of [10] and [11] we present a new class of lookback options (by first studying the canonical ‘Russian’ variant) where the holder enjoys the early exercise feature of American options whereupon his payoff (deliverable immediately) is the ‘best prediction’ of the European payoff under the hypothesis that the true drift of the stock price equals a contract drift. I...

The Russian option: Finite horizon

We show that the optimal stopping boundary for the Russian option with finite horizon can be characterized as the unique solution of a nonlinear integral equation arising from the early exercise premiumrepresentation (an explicit formula for the arbitrage-free price in terms of the optimal stopping boundary having a clear economic interpretation). The results obtained stand in a complete parall...

Filling the Gap between American and Russian Options: Adjustable Regret

A Reduced Basis for Option Pricing

We introduce a reduced basis method for the efficient numerical solution of partial integro-differential equations which arise in option pricing theory. Our method uses a basis of functions constructed from a sequence of Black-Scholes solutions with different volatilities. We show that this choice of basis leads to a sparse representation of option pricing functions, yielding an approximation w...