Keeping the option when the continuation value is larger than the amount received on exercise, and exercising when that amount is at least the continuation value, is the policy that maximizes the option's value1. When valuing from paths, it is estimated by the regression in least-squares Monte Carlo.

Consider a hypothetical example of a put option with a strike price of 110 yen, when the underlying asset's price is 90 yen. The amount received on exercise is 20 yen. If the continuation value is estimated at 18 yen, the holder exercises. If it is estimated at 23 yen, the holder keeps the option.

Notes

  1. Longstaff and Schwartz (2001), page 121 (Section 2.1). Lyuu's lecture notes, Page 927, describe the continuation value as the conditional expectation of the payoff from keeping the option alive. ↩