The British Asian Option

Abstract

Following the economic rationale of Peskir and Samee (2008a,b), we present a new class of Asian options where the holder enjoys the early exercise feature of American options whereupon his payoff (deliverable immediately) is the ‘best prediction’ of the European payoff under the hypothesis that the true drift of the stock price equals a contract drift. Inherent in this is a protection feature that is key to the British Asian option. Should the option holder believe the true drift of the stock price to be unfavorable (based upon the observed price movements), he can substitute the true drift with the contract drift and minimize his losses. The practical implications of this protection feature are most remarkable, as not only is the option holder afforded a unique protection against unfavorable stock price movements (covering the ability to sell in a liquid option market completely endogenously), but also when the stock price movements are favorable he will generally receive high returns. We derive a closed form expression for the arbitrage-free price in terms of the rational exercise boundary and show that the rational exercise boundary itself can be characterized as the unique solution to a nonlinear integral equation. Using these results we perform a financial analysis of the British Asian option that leads to the conclusions above and shows that with the contract drift properly selected the British Asian option becomes a very attractive alternative to the classic (European) Asian option.

Keywords:

• American Asian option
• Arbitrage-free price
• Arithmetic/geometric average
• British Asian option
• European Asian option
• Fixed/floating strike
• Flexible Asian options
• Geometric Brownian motion
• Liquid/illiquid market
• Local time-space calculus
• Nonlinear integral equation
• Optimal stopping
• Parabolic free-boundary problem
• Rational exercise boundary
• The Shiryaev process

Subject Classification:

• Primary 91B28, 60G40
• Secondary 35R35, 45G10, 60J60

Notes

The values in the left-hand column represent the position of the process X = I/S. The returns are expressed as a percentage of the original option price paid by the buyer (rounded to the nearest integer), i.e., R(t, x)/100 =G ^{μ _c} (t, x)/V(0, 0) and R _E (t, x)/100 =V _E (t, x)/V _E (0, 0), respectively. The parameter set is T = 1, r = 0.1, σ = 0.4, and the contract drift μ _c equals −0.1 so that b(0) = 0.99 (recall Figure 1 above). The actual returns depend explicitly upon the stock price S _t in relation to its initial value S ₀ and can be recovered by multiplying the tabulated returns by S _t /S ₀. The returns shown are sufficient for comparative purposes.

Recommended by A. G. Tartakovsky