Abstract
This study proposes a strategy to make the lookback option cheaper and more practical, and suggests the use of its properties to reduce risk exposure in cryptocurrency markets through blockchain enforced smart contracts and correct for informational inefficiencies surrounding prices and volatility. This paper generalizes partial, discretely-monitored lookback options that dilute premiums by selecting a subset of specified periods to determine payoff, which we call amnesiac lookback options. Prior literature on discretely-monitored lookback options considers the number of periods and assumes equidistant lookback periods in pricing partial lookback options. This study by contrast considers random sampling of lookback periods and compares resulting payoff of the call, put and spread options under floating and fixed strikes. Amnesiac lookbacks were priced with Monte Carlo simulations of Gaussian random walks under equidistant and random periods. Results were compared to analytic and binomial pricing models for the same derivatives. Simulations show diminishing marginal increases to the fair price as the number of selected periods is increased. The returns correspond to a Hill curve whose parameters are set by interest rate and volatility. We demonstrate over-pricing under equidistant monitoring assumptions with error increasing as the lookback periods decrease. An example of a direct implication for event trading is when shock is forecasted but its timing uncertain, equidistant sampling produces a lower error on the true maximum than random choice. We conclude that the instrument provides an ideal space for investors to balance their risk, and as a prime candidate to hedge extreme volatility. We discuss the application of the amnesiac lookback option and path-dependent options to cryptocurrencies and blockchain commodities in the context of smart contracts.
Highlights
Lookback options have been a prototypical example of exotic options within the financial literature [1]
Lookback options are immensely useful instruments for the use of hedging against risks associated with high volatility and notably effective at canceling investor regret as well
We suggest the use and exploration of a new form of partial lookback, the amnesiac lookback option, that can look back upon any discretely selected period prior to expiration
Summary
Lookback options have been a prototypical example of exotic options within the financial literature [1]. The option gives the holder the right to buy or sell an underlying asset at any price attained within a specified “lookback” period. The payoff of a lookback call (put) is the difference between the underlying price at maturity and the maximum (minimum) price attained. The trader is able to capitalize on the underlying asset as if he sold it at the optimal time. By utilizing only the highest value of the underlying asset in determining payoff, lookback options capture the best case scenarios that people would like to sell at, but often miss due to uncertainty. By corresponding payoffs to the extreme movements of underlying asset prices, lookback options allow for investors to hedge against or invest in volatility
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