TITLE

# Pricing a contingent claim liability with transaction costs using asymptotic analysis for optimal investment

AUTHOR(S)
Bichuch, Maxim
PUB. DATE
July 2014
SOURCE
Finance & Stochastics;Jul2014, Vol. 18 Issue 3, p651
SOURCE TYPE
DOC. TYPE
Article
ABSTRACT
We price a contingent claim liability (claim for short) using a utility indifference argument. We consider an agent with exponential utility, who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of a proportional transaction cost Îµ>0 in two cases: with and without a claim. Using the heuristic computations of Whalley and Wilmott (Math. Finance 7:307-324, ), under suitable technical conditions, we provide a rigorous derivation of the asymptotic expansion of the value function in powers of $\varepsilon^{\frac{1}{3}}$ in both cases with and without a claim. Additionally, using the utility indifference method, we derive the price of the claim at the leading order of $\varepsilon^{\frac{2}{3}}$. In both cases, we also obtain a 'nearly optimal' strategy, whose expected utility asymptotically matches the leading terms of the value function. We also present an example of how this methodology can be used to price more exotic barrier-type contingent claims.
ACCESSION #
97072646

## Related Articles

• Asymptotic arbitrage with small transaction costs. Klein, Irene; Lépinette, Emmanuel; Perez-Ostafe, Lavinia // Finance & Stochastics;Oct2014, Vol. 18 Issue 4, p917

We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for a sequence of financial markets with small proportional transaction costs Î» on market n, in terms of contiguity properties of sequences of equivalent probability measures...

• OPTIMAL DIVIDEND PROBLEMS FOR A JUMP-DIFFUSION MODEL WITH CAPITAL INJECTIONS AND PROPORTIONAL TRANSACTION COSTS. CHUANCUN YIN; KAM CHUEN YUEN // Journal of Industrial & Management Optimization;Oct2015, Vol. 11 Issue 4, p1247

In this paper, we study the optimal control problem for a company whose surplus process evolves as an upward jump diffusion with random return on investment. Three types of practical optimization problems faced by a company that can control its liquid reserves by paying dividends and injecting...

• Mean square error for the Leland-Lott hedging strategy: convex pay-offs. Denis, Emmanuel; Kabanov, Yuri // Finance & Stochastics;2010, Vol. 14 Issue 4, p625

Leland's approach to the hedging of derivatives under proportional transaction costs is based on an approximate replication of the European-type contingent claim V using the classical Black-Scholes formula with a suitably enlarged volatility. The formal mathematical framework is a scheme of...

• The asymptotic expansion for a class of non-linear singularly perturbed problems with optimal control. Han Xu; Yinlai Jin // Journal of Nonlinear Sciences & Applications (JNSA);2016, Vol. 9 Issue 5, p2718

In this article, we discuss a class of three-dimensional non-linear singularly perturbed systems with optimal control. Firstly, we confirm the existence of heteroclinic orbits connecting two equilibrium points about their associated systems by necessary conditions of optimal control and...

• OPTIMAL PRICING POLICY FOR DETERIORATING ITEMS WITH PRESERVATION TECHNOLOGY INVESTMENT. JIANXIONG ZHANG; ZHENYU BAI; WANSHENG TANG // Journal of Industrial & Management Optimization;Oct2014, Vol. 10 Issue 4, p1261

This paper considers the problem of simultaneously determining the price and inventory control strategies for deteriorating items. It is assumed that the rate of deterioration can be reduced by means of effective preservation technology investment and the demand rate is a function of selling...

• Simulation and optimization in marketing: Optimal control of consumer goodwill, price and investment. Raczynski, Stanislaw // International Journal of Modeling, Simulation & Scientific Compu;Sep2014, Vol. 5 Issue 3, p-1

Dynamic market optimization with respect to price, advertisement and investment is presented. The market model is nonlinear. Its main parameters are the elasticities with respect to price, advertisement and consumer income. Dynamic elements has been added to the static model based on the market...

• An Integer Programming Model for Pricing American Contingent Claims under Transaction Costs. Pınar, M.; Camcı, A. // Computational Economics;Jan2012, Vol. 39 Issue 1, p1

We study the problem of computing the lower hedging price of an American contingent claim in a finite-state discrete-time market setting under proportional transaction costs. We derive a new mixed-integer linear programming formulation for calculating the lower hedging price. The linear...

• Market Crashes and Informational Avalanches. Lee, In Ho // Review of Economic Studies;Oct98, Vol. 65 Issue 4, p741

This paper analyses a security market with transaction costs and a sequential trading structure. Transaction costs may prevent many traders from revealing their private information if they trade in a sequential fashion. Due to the information aggregation failure, hidden information gets...

• Some New Evidence on the Profitability of One-Way versus Round-Trip Arbitrage. WOODWARD, R. S. // Journal of Money, Credit & Banking (Ohio State University Press);Nov88, Vol. 20 Issue 4, p645

This article focuses on the transaction cost bands associated with both round-trip arbitrage and one-way arbitrage and the research that demonstrates that neutral trading bands associated with transaction costs are narrower than the bands associated with two-way or round-trip arbitrage. This...

Share