Abstract
In this paper an extension of the well-known binomial approach to option pricing is presented. The classical question is: What is the price of an option on the risky asset? The traditional answer is obtained with the help of a replicating portfolio by ruling out arbitrage. Instead a two-person game from the Nash equilibrium of which the option price can be derived is formulated. Consequently both the underlying asset’s price at expiration and the price of the option on this asset are endogenously determined. The option price derived this way turns out, however, to be identical to the classical no-arbitrage option price of the binomial model if the expiration-date prices of the underlying asset and the corresponding risk-neutral probability are properly adjusted according to the Nash equilibrium data of the game.
Highlights
Traditional option pricing is based on the assumption that risk management is a single person decision game
The classical option pricing question in this framework is: What is the timezero price of an option on the risky asset? The traditional answer is obtained with the help of a replicating portfolio by ruling out arbitrage
What is the market price of the option considered? the standard approach of option pricing.6 briefly reviewed There are two basic components to be taken into consideration: the concept of perfect arbitrage and the no arbitrage principle
Summary
Traditional option pricing is based on the assumption that risk management is a single person decision game. The game-theoretic option price derived this way turns out, to be identical to the classical no-arbitrage option price of the single-period binomial model if the expiration-date prices of the underlying asset and the corresponding risk-neutral probability are properly adjusted. Economics and Business Review, Vol 6 (20), No 3, 2020 according to the Nash-equilibrium data of the game In this sense the model of the paper can be considered as an extension of the classical binomial framework opening the latter for interpersonal decision making. The insurance company is able to pursue their interests by independently choosing the investment strategy This way the insurance company as seller of the (implicit) put option affects the underlying value on the maturity date; i.e., the rate of return on the investment portfolio.
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