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This question is most relevant to the evaluation of embedded options, such as the refinancing option granted to borrowers in the mortgage and bank loan markets, or the call option present in some corporate bonds, than to exchange traded options.

Much more so than market participants in exchange traded options, which have purely market-based incentives, the borrowers and issuing entities which are granted embedded options often employ sub-optimal (irrational) exercise strategies. Sometimes, these only appear irrational to the lender/investor, when, in fact, they are optimal when considering other factors such as the borrower's personal financial condition or other factors (such as a homeowner's desire to move to a new house). In those cases, the difficulty from the modeler's perspective is that these factors are unobservable, and, hence, must be modeled as random. Other times, decision makers make truly sub-optimal decisions based on a private evaluation of the value of exercise that differs from a "correct" market-implied decision rule.

Which modeling approach leads to better predictions and better relative value measures?

  • Rational: Option-holder follows a fully rational and optimal exercise strategy when deciding whether or not to exercise his option. The modeler attempts to reproduce the holder's payoff function as faithfully as possible.
  • Behavioral: Option-holder follows a simple reduced-form exercise strategy which may lead to sub-optimal decisions. The modeler attempts to estimate the parameters of the exercise strategy, either from market data or from historical experience.

Under the rational approach, how do you treat unobserved characteristics? Does the presence of unobserved characteristics make the rational approach ultimately equivalent to a market-implied behavioral approach? Is it even possible to fit the unobserved information directly to market data?

Open-ended Bounty Offer: We may not yet have a broad enough user base familiar with the pricing and modeling of embedded options to adequately answer this question. As such, I pledge to offer a bounty of 100 points to any user who can adequately answer this question. If you are a new user and you have come to this question long after activity has died down, then so long as I am still active on this site my offer remains in effect.

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1 Answer

honestly your question is hard to understand. Are these two questions the same?

  1. "Does fitting sub-optimal option exercise strategies to market data yield better option values?"
  2. "which modeling approach leads to better predictions and better relative value measures?"

I think you want to ask 1 and I think it is similar to Setting the r in put-call parity? The variables C, P, S, and T−t are directly observable in the market place and contract definition. r is unobservable and it will definitely affect a deep ITM put holder's optimal early exercise strategy.

Likewise here, I think which model you use depends on your purpose. Both model has its merit and application.

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Hi Ian, welcome to quant.SE and thanks for attempting an answer. Yes, the two questions are the same. One of the modeling approaches is to fit a sub-optimal exercise strategy, the other is to assume fully rational exercise. The end goal of either approach is to construct option values, which are used as part of a relative value model. I am dealing with embedded options, markets in which C or P (the option prices/values) are not directly observable, so it is quite a different problem from setting an unobservable interest rate in an exchange-traded option pricing problem. – Tal Fishman Dec 10 '11 at 22:46
I still don't get the idea? Sorry not help much. Thanks for the welcome anyway. – Ian Dec 11 '11 at 9:59

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