On Approximate Pricing of Spread Options via Conditional Value-at-Risk

C Maksimov,A Melnikov

doi:10.26794/2308-944x-2021-9-3-27-51

Abstract

It is widely accepted to use conditional value-at-risk for risk management needs and option pricing. As a rule, there are difficulties in exact calculations of conditional value-at-risk. In the paper, we use the conditional value-at-risk methodology to price spread options, extending some approximation approaches for these needs. Our results we illustrate by numerical calculations which demonstrate their effectiveness. We also show how conditional value-at-risk pricing can help with regulatory needs inspired by the Basel Accords.

Highlights

1 Introduction In complete markets, every contingent claim is replicable in the class of self-financing strategies, and its price is unique
There is a whole range of arbitrage-free prices in incomplete markets or in markets with constraints
This paper aims to take a step in the direction of generalising the results obtained by Melnikov and Smirnov (2012) and consider the problem of CVaR-based option pricing within the context of the Margrabe market model with two risky assets

Summary

Introduction

Every contingent claim is replicable in the class of self-financing strategies, and its price is unique. The author considered a market setting with several risky securities and determined the optimal policy that maximises the probability of reaching a certain level of wealth before some fixed terminal time Working in this direction, Foellmer and Leukert (1999) transformed the initial problem into the problem when an optimal strategy maximises the probability of successful hedging. Melnikov and Smirnov (2012) applied the ideas of Foellmer and Leukert (2000) to the case where CVaR represents the loss function l that models the attitude of an agent to risk and considered the following dual problem: minimisation of CVaR when the initial capital is bounded from above, and minimisation of hedging costs subject to a constraint of the amount of CVaR. CVaR is chosen as the measure of risk to make the paper’s results applicable by practitioners in the industry

Preliminaries and Existing Approximating Methods

Main Results

Conclusion