A multiscale extension of the Margrabe formula under stochastic volatility

Jeong-Hoon Kim, Chang Rae Park

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

The pricing of financial derivatives based on stochastic volatility models has been a popular subject in computational finance. Although exact or approximate closed form formulas of the prices of many options under stochastic volatility have been obtained so that the option prices can be easily computed, such formulas for exchange options leave much to be desired. In this paper, we consider two different risky assets with two different scales of mean-reversion rate of volatility and use asymptotic analysis to extend the classical Margrabe formula, which corresponds to a geometric Brownian motion model, and obtain a pricing formula under a stochastic volatility. The resultant formula can be computed easily, simply by taking derivatives of the Margrabe price itself. Based on the formula, we show how the stochastic volatility corrects the Margrabe price behavior depending on the moneyness and the correlation coefficient between the two asset prices.

Original languageEnglish
Pages (from-to)59-65
Number of pages7
JournalChaos, Solitons and Fractals
Volume97
DOIs
Publication statusPublished - 2017 Apr 1

Fingerprint

Stochastic Volatility
Pricing
Computational Finance
Financial Derivatives
Mean Reversion
Geometric Brownian Motion
Stochastic Volatility Model
Asymptotic Analysis
Correlation coefficient
Volatility
Closed-form
Derivative

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

@article{f4ddc5b0761a446db67eb8470c130857,
title = "A multiscale extension of the Margrabe formula under stochastic volatility",
abstract = "The pricing of financial derivatives based on stochastic volatility models has been a popular subject in computational finance. Although exact or approximate closed form formulas of the prices of many options under stochastic volatility have been obtained so that the option prices can be easily computed, such formulas for exchange options leave much to be desired. In this paper, we consider two different risky assets with two different scales of mean-reversion rate of volatility and use asymptotic analysis to extend the classical Margrabe formula, which corresponds to a geometric Brownian motion model, and obtain a pricing formula under a stochastic volatility. The resultant formula can be computed easily, simply by taking derivatives of the Margrabe price itself. Based on the formula, we show how the stochastic volatility corrects the Margrabe price behavior depending on the moneyness and the correlation coefficient between the two asset prices.",
author = "Jeong-Hoon Kim and Park, {Chang Rae}",
year = "2017",
month = "4",
day = "1",
doi = "10.1016/j.chaos.2017.02.006",
language = "English",
volume = "97",
pages = "59--65",
journal = "Chaos, Solitons and Fractals",
issn = "0960-0779",
publisher = "Elsevier Limited",

}

A multiscale extension of the Margrabe formula under stochastic volatility. / Kim, Jeong-Hoon; Park, Chang Rae.

In: Chaos, Solitons and Fractals, Vol. 97, 01.04.2017, p. 59-65.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A multiscale extension of the Margrabe formula under stochastic volatility

AU - Kim, Jeong-Hoon

AU - Park, Chang Rae

PY - 2017/4/1

Y1 - 2017/4/1

N2 - The pricing of financial derivatives based on stochastic volatility models has been a popular subject in computational finance. Although exact or approximate closed form formulas of the prices of many options under stochastic volatility have been obtained so that the option prices can be easily computed, such formulas for exchange options leave much to be desired. In this paper, we consider two different risky assets with two different scales of mean-reversion rate of volatility and use asymptotic analysis to extend the classical Margrabe formula, which corresponds to a geometric Brownian motion model, and obtain a pricing formula under a stochastic volatility. The resultant formula can be computed easily, simply by taking derivatives of the Margrabe price itself. Based on the formula, we show how the stochastic volatility corrects the Margrabe price behavior depending on the moneyness and the correlation coefficient between the two asset prices.

AB - The pricing of financial derivatives based on stochastic volatility models has been a popular subject in computational finance. Although exact or approximate closed form formulas of the prices of many options under stochastic volatility have been obtained so that the option prices can be easily computed, such formulas for exchange options leave much to be desired. In this paper, we consider two different risky assets with two different scales of mean-reversion rate of volatility and use asymptotic analysis to extend the classical Margrabe formula, which corresponds to a geometric Brownian motion model, and obtain a pricing formula under a stochastic volatility. The resultant formula can be computed easily, simply by taking derivatives of the Margrabe price itself. Based on the formula, we show how the stochastic volatility corrects the Margrabe price behavior depending on the moneyness and the correlation coefficient between the two asset prices.

UR - http://www.scopus.com/inward/record.url?scp=85013767556&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85013767556&partnerID=8YFLogxK

U2 - 10.1016/j.chaos.2017.02.006

DO - 10.1016/j.chaos.2017.02.006

M3 - Article

AN - SCOPUS:85013767556

VL - 97

SP - 59

EP - 65

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

ER -