Model uncertainty and the pricing of American options

Abstract

This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract The virtue of an American option is that it can be exercised at any time. This right is particularly valuable when there is model uncertainty. Yet almost all the extensive literature on American options assumes away model uncertainty. This paper quantifies the potential value of this flexibility by identifying the supremum on the price of an American option when we do not impose a model, but rather consider the class of all models which are consistent with a family of European call prices. The bound is enforced by a hedging strategy involving these call options which is robust to model error. Permanent

Super-Hedging American Options With Semi-Static Trading Strategies Under Model Uncertainty

“…Moreover, the true state i is revealed at the beginning only to Nature, not to the hedger. In Bayraktar et al (2015), Hobson & Neuberger (2016), it is pointed out that the super-pricing price (hedger's price) can be strictly greater than the highest model based price (Nature's price). That is, it is possible that…”

“…In contrast Hobson & Neuberger (2017), Nature can have all sorts of information as long as the models appears to be consistent to the hedger (note that the hedger only knows the information generated by the stock). To be more precise, the authors of Hobson & Neuberger (2017) call a filtered probability space M = (Ω , F = (F t ) t=0,... ,T , Q ) a consistent model if the space (Ω , F ) supports a stochastic process S (and random vector g), S is a (Q , F )-martingale, and…”

“…To be more precise, the authors of Hobson & Neuberger (2017) call a filtered probability space M = (Ω , F = (F t ) t=0,... ,T , Q ) a consistent model if the space (Ω , F ) supports a stochastic process S (and random vector g), S is a (Q , F )-martingale, and…”

“…other models proposed in Hobson & Neuberger (2017) are redundant. Our result also generalizes the example provided in Hobson & Neuberger (2016) that the highest model based price can be considered as a randomization over models.…”

“…In the next section, we provide the setup and the main result. In Section 3, we give a discussion for the results in Bayraktar et al (2015), Hobson & Neuberger (2017), and this paper. Finally, we provide the proof for the main result in Section 4.…”