Equal Risk Pricing Under Convex Trading Constraints

21 Pages Posted: 24 Jun 2015 Last revised: 30 Dec 2015

See all articles by Ivan Guo

Ivan Guo

Monash University - School of Mathematical Sciences

Song-Ping Zhu

University of Wollongong

Date Written: December 20, 2015

Abstract

In an incomplete market model where convex trading constraints are imposed upon the underlying assets, it is no longer possible to obtain unique arbitrage-free prices for derivatives using standard replication arguments. Most existing derivative pricing approaches involve the selection of a suitable martingale measure or the optimisation of utility functions as well as risk measures from the perspective of a single trader.

We propose a new and effective derivative pricing method, referred to as the equal risk pricing approach, for markets with convex trading constraints. The approach analyses the risk exposure of both the buyer and seller of the derivative, and seeks an equal risk price which evenly distributes the expected loss for both parties under optimal hedging. The existence and uniqueness of the equal risk price are established for both European and American options. Furthermore, if the trading constraints are removed, the equal risk price agrees with the standard arbitrage-free price.

Finally, the equal risk pricing approach is applied to a constrained Black-Scholes market model where short-selling is banned. In particular, simple pricing formulas are derived for European calls, European puts and American puts.

Keywords: derivative pricing, trading constraints, risk measures, short selling ban

Suggested Citation

Guo, Ivan and Zhu, Song-Ping, Equal Risk Pricing Under Convex Trading Constraints (December 20, 2015). Available at SSRN: https://ssrn.com/abstract=2622037 or http://dx.doi.org/10.2139/ssrn.2622037

Ivan Guo (Contact Author)

Monash University - School of Mathematical Sciences ( email )

Clayton Campus
Victoria, 3800
Australia

Song-Ping Zhu

University of Wollongong ( email )

Northfield Ave.
Wollongong, NSW
Australia
61-2-42213807 (Phone)

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