Bid-ask American option pricing under Dempster-Shafer uncertainty
The aim is to model a discrete-time market under ambiguity, formed by a frictionless risk-free bond and a non-dividend paying stock with bid-ask spread. To model the stock bid price evolution, we refer to the notion of Markov and time-homogeneous multiplicative binomial process under Dempster-Shafer uncertainty, that is introduced in [1]. For a European derivative, we generalize the classical binomial pricing formula [2] by allowing for bid-ask prices and investigate the properties of the ensuing replicating strategies. Next, for an American derivative, we propose a backward bid-ask pricing procedure and prove that the resulting discounted price processes are the bid-ask Choquet-Snell envelopes of the discounted payoff process, respectively. Moreover, for an American call option, we prove a generalization of the well-known Merton’s theorem [3] holding for both the bid and the ask price processes. Finally, we propose a market consistent calibration procedure and show the use of the calibrated model in bid-ask option pricing. REFERENCES [1] A. Cinfrignini, D. Petturiti, B. Vantaggi, Dynamic bid-ask pricing under Dempster-Shafer uncertainty, Journal of Mathematical Economics, 107(2023), 102871. [2] J. Cox, S. Ross, M. Rubinstein, Option pricing: A simplified approach, Journal of Financial Economics, 7(1979), 229–263. [3] R.C. Merton, Theory of Rational Option Pricing, The Bell Journal of Economics and Management Science, 4(1973), 141–183.
Area: CS44 - Algebraic option pricing and probability: in honor of Peter Carr (Umberto Cherubini and Sabrina Mulinacci)
Keywords: Bid-Ask prices, Choquet pricing rule, Imprecise stochastic processes
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