Choosing Yield Curves for Equity Option Forward Prices

Summary

The document asks how to choose rates and yield curves when constructing an SSVI volatility surface for single stocks and equity indices. After deriving forward prices from listed options, the researcher must infer dividends, but the result depends on which yield assumptions are used. The question contrasts estimating separate risk-free, funding, repo, and borrow curves and combining them with using risk-free rates while letting implied dividends absorb other effects.

It highlights a practical distinction between the curve used to determine forwards and the curve used to discount derivative payoffs. Whether separate curves are needed depends on the pricing framework: a surface calibration may only require forward prices, while a model that separately represents financing and discounting may need distinct inputs. The document poses this issue but offers no answer, market convention, or empirical comparison, so it serves as a modeling question rather than evidence for one approach.

Key ideas

• Forward prices and inferred dividends depend on the yield assumptions used in option calibration.
• Risk-free, funding, repo, and borrow rates may be represented as separate curves.
• An implied dividend estimate can absorb effects omitted from the chosen yield curve.
• The need for separate curves depends on how a pricing model uses forwards and discounting.

Tags

# Yield curves for vol surface construction


# Yield curves for vol surface construction












Assuming I want to calibrate an SSVI surface for single stocks and equity indices, I clean/retrieve listed option prices and deduct implied Forward prices. Once I have Forward prices, and if I already have some yield curve, I can back out the corresponding implied dividends.

As we know that in practice banks may quote options using discount (risk-free) yield, funding yield (in excess of risk-free) and repo and borrow yield, is it common practice to

- first somehow estimate these various yield curves separately and sum them to get the "yield curve" to be used in the Forward prices, or

- would one instead just use risk-free rates as "yield curve" and then assume that the implied div backed out is already including all other params (funding, borrow etc)?

Is there any point in having separate curves for these or is that only model dependent (e.g. not needed for SSVI as we only want a Forward price, but needed for pricing models where the yield curve used for payoff discounting and the rates inside the Forward are not the same)?

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