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Approximating Spread-Option Hedges with Calls on Each Asset

Article Quant Q&A · Author: glork
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Summary

The document asks how to hedge a spread option whose payoff depends on the difference between two assets using only calls written on each asset and cash. The question describes a Black–Scholes setting and a direct hedge based on the option price sensitivities to both underlyings, then asks how to replicate or approximate that hedge with calls instead of the underlying shares.

No answer or worked construction is included, so the document does not establish a specific call-based hedge, its cost, or its effectiveness. Its useful focus is the distinction between a spread payoff involving two assets and a portfolio made from vanilla options on the individual assets. Any proposed hedge would need to account for the relationship between the assets, option strikes and maturities, and the changing sensitivities of the spread option; these details are not supplied. The question is best treated as a prompt for further analysis rather than a complete hedging method.

Key ideas

  • A spread option pays according to the difference between two underlying asset prices.
  • The question considers replacing direct exposure to both assets with calls on each asset and cash.
  • The described Black–Scholes sensitivities provide a direct underlying hedge but do not specify a call-based replication.
  • The document gives no worked hedge or evidence about its cost or performance.

Tags

OptionsDerivatives pricingRisk management
Full text
# hedging of a spread option with call


# hedging of a spread option with call












We have 2 underlying $S^{1}$ and $S^{2}$ with BS dynamic under the risk-neutral measure (r constant...) I found the (big) PDE satisfied by the price function $u(t,x,y)$ of a call spread whose payoff is $(S_{T}^{1}-S_{T}^{2}-K)_{+}]$ Then I have deduced the number of shares of $S^{1}$ and $S^{1}$ and the amount of cash to hedge this option (to hold $du/dx$ shares $S^{1}$ ...) My question is: how to hedge this spread option with only a call written on $S^{1}$, a call written on $S^{2}$ and cash ?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.