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Correlation risk, cross‐market derivative products and portfolio performance

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  • T. S. Ho
  • Richard C. Stapleton
  • Marti G. Subrahmanyam

Abstract

We consider portfolios whose returns depend on at least three variables and show the effect of the correlation structure on the probabilities of the extreme outcomes of the portfolio return, using a multivariate binomial approximation. the portfolio risk is then managed by using derivatives. We illustrate this risk management both with simple options, whose payoff depends upon only one of the underlying variables, and with more complex instruments, whose payoffs (and values) depend upon the correlation structure The question of benchmarking portfolio performance is complicated by the use of derivatives, especially complex derivatives, since these instruments fundamentally alter the distribution of returns. We use the multivariate binomial model to set performance benchmarks for multicurrency, international portfolios. Our model is illustrated using a simple example where a German institution invests a proportion of its funds in Germany equities and the remainder in UK equities. Portfolio performance is measured in Deutsche Marks and depends upon (1) the DAX index, (2) the FTSE index and (3) the Deutsche Mark‐Sterling exchange rate. The output of the model is a simulation of possible outcomes from the portfolio hedging strategy. the difference in our methodology is that we are able to retain the simplicity of the binomial distribution, used extensively in the analysis of options, in a multivariate context. This is achieved by building three (or more) binomial trees for the individual variables and capturing the correlation structure with the use of varying conditional probabilities.

Suggested Citation

  • T. S. Ho & Richard C. Stapleton & Marti G. Subrahmanyam, 1995. "Correlation risk, cross‐market derivative products and portfolio performance," European Financial Management, European Financial Management Association, vol. 1(2), pages 105-124, July.
  • Handle: RePEc:bla:eufman:v:1:y:1995:i:2:p:105-124
    DOI: 10.1111/j.1468-036X.1995.tb00011.x
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    References listed on IDEAS

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    1. Nelson, Daniel B & Ramaswamy, Krishna, 1990. "Simple Binomial Processes as Diffusion Approximations in Financial Models," The Review of Financial Studies, Society for Financial Studies, vol. 3(3), pages 393-430.
    2. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
    3. Amin, Kaushik I., 1991. "On the Computation of Continuous Time Option Prices Using Discrete Approximations," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(4), pages 477-495, December.
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    Cited by:

    1. Caporin, Massimiliano & Preś, Juliusz & Torro, Hipolit, 2012. "Model based Monte Carlo pricing of energy and temperature Quanto options," Energy Economics, Elsevier, vol. 34(5), pages 1700-1712.
    2. Xu, Weidong & Wu, Chongfeng & Li, Hongyi, 2011. "Accounting for the impact of higher order moments in foreign equity option pricing model," Economic Modelling, Elsevier, vol. 28(4), pages 1726-1729, July.
    3. Raquel Fonseca & Wolfram Wiesemann & Berç Rustem, 2012. "Robust international portfolio management," Computational Management Science, Springer, vol. 9(1), pages 31-62, February.
    4. Rodwell Kufakunesu & Farai Mhlanga, 2018. "On the sensitivity analysis of energy quanto options," Papers 1810.06335, arXiv.org.
    5. Foad Shokrollahi, 2016. "Subdiffusive fractional Brownian motion regime for pricing currency options under transaction costs," Papers 1612.06665, arXiv.org, revised Aug 2017.
    6. Sun, Qi & Xu, Weidong, 2015. "Pricing foreign equity option with stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 89-100.
    7. Foad Shokrollahi & Adem Kılıçman & Marcin Magdziarz, 2016. "Pricing European options and currency options by time changed mixed fractional Brownian motion with transaction costs," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(01), pages 1-22, March.
    8. Xu, Weidong & Wu, Chongfeng & Li, Hongyi, 2011. "Foreign equity option pricing under stochastic volatility model with double jumps," Economic Modelling, Elsevier, vol. 28(4), pages 1857-1863, July.

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