Lookback Straddle

Twizel, Canterbury, New Zealand
Twizel, Canterbury, New Zealand

A lookback straddle is an option strategy composed of a lookback call option and a lookback put option. The former grants its holder the right to buy an asset at the lowest price observed during the lifetime of the option while the latter grants its holder the right to sell the same asset at the highest price observed during the lifetime of the option.

A lookback straddle thus enables the investor to “buy low and sell high.” Goldman et al. (1979) discuss a closed-form solution for its Black–Scholes no-arbitrage price.

Among option strategies, the lookback straddle is of particular interest due to its close connection to the return profile of trend-following hedge funds. More specifically, the majority of commodity trading advisers, or managed futures funds, are “trend followers.”

So-called primitive trading strategies (PTS) capture the essence of such dynamic trading strategies using static easy-to-understand algorithms. For example, the payoff of a perfect market timer who may only take a long position should be identical to the payoff from holding a call option.

If, on the other hand, it is possible to go long or short, the perfect trend follower should “buy low and sell high,” which exactly corresponds to the payoff of a lookback straddle. Consequently, the lookback straddle can be thought of as the PTS used by market timers.