The Russian Option: Reduced Regret
The Russian Option: Reduced Regret
A Russian option is a perpetual American-type option that pays the owner upon exercise the historical maximum price of the stock (this is supposed to "reduce the regret" of not exercising the option at the right time). The option was invented by L. Shepp and A. N. Shirayev and named "the Russian option". Although it is not traded in practice, several remarkable formulas for the option value, optimal exercise time, and the expected exercise time (under the assumption that the stock follows the Black–Scholes model) have been found and have had an important impact on probability theory.
In this Demonstration the orange line shows the movement of a single path of stock prices. You can choose whether the actual or discounted stock price should be shown. The initial stock price is fixed at 100. The blue dot on the vertical axis is the strike price, which you can vary. The blue line shows the discounted option payoff: it splits into two branches when the option is exercised—one, the horizontal line shows the discounted payoff after exercise; the other shows the value of the discounted payoff should you choose not to exercise the option. The horizontal black line shows the option value computed with the Shepp–Shirayev formula and the blue dot on the horizontal axis shows the expected exercise time found by Graversen and Peskir.
Mouseover the lines in the Demonstration to see what they represent.