Created by Dr. Jan-Frederik Mai

Can we retrieve the equity forward from American option prices?

The equity forward with a given maturity is defined as today’s risk-neutral expectation of a stock price at maturity. If arbitrage-free prices for European put and call options with the given maturity are observed for different strike prices, the equity forward can be retrieved from the put-call parity. In particular, it is invariant with respect to different risk-neutral pricing measures which explain observed option prices, i.e. it is a model-free quantity. More precisely, the equity forward is given by the unique root of the (in practice partially) observed difference between calls and puts, viewed as a function in the strike price. In contrast, if only American-style put and call option prices are observed, the lack of a put-call parity makes it more difficult to retrieve the equity forward in an unambiguous way from the observed option data. In particular, the unique root of the difference between calls and puts in general is no longer equal to the equity forward. The present article investigates whether American-style put and call prices also determine the equity forward unambiguously. Unfortunately, this seemingly simple “yes or no”-question appears to be non-trivial and open, and the present investigation is not able to answer it.


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