Why an Autocallable Bond Cannot Match an Issuer’s Optimal Call
Summary
The document considers whether varying the autocall level of an autocallable bond can reproduce the value of an issuer-callable bond priced with an optimal exercise policy. It explains that the issuer-callable bond is no more valuable than an autocallable structure with a predetermined call rule: the issuer can always choose a fixed decision in advance, while an optimal policy can respond to evolving market conditions.
Varying autocall levels, potentially by date, may identify the least-valued structure within that restricted family, but its value remains at least as high as the issuer-callable value and is typically higher. The gap reflects the flexibility of path-dependent exercise decisions, which may depend on rates, credit conditions, and volatility. The answer gives a conceptual dominance argument rather than a numerical calibration method or a model-specific proof of strict inequality.
Key ideas
- A predetermined autocall rule is a restricted form of the issuer’s broader call decision.
- Optimizing autocall levels can find the lowest value within that family of rules.
- The autocallable value is at least as high as the issuer-callable bond value.
- Path-dependent exercise flexibility can depend on interest rates, credit conditions, and volatility.
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# How to spot optimal exercise level of issuer-callable bonds with autocallable bonds call level? # How to spot optimal exercise level of issuer-callable bonds with autocallable bonds call level? I'm looking for a bit more background on a question that came up here: Our traders use some sort of Longstaff-Schwartz to calculate the optimal point when to call an issuer-callable bond. My question is: Does anyone know whether a) it' s possible and b) how to exactly locate the optimal exercise point by systematically varying the autocall-level of an autocallable bond? I mean shouldn't the autocall PV coincide with the issuer-callable PV if the autocallable-level meets this optimal exercise level in an issuer-callable bond? My guess is that "left" and "right" of this optimum, the autocall-PV is always above the issuer-callable PV and coincides with its minimum when autocallable-PV = issuercallable PV? Happy to hear your thoughts on this.. Thomas ## Answer by dm63 (score 1, accepted) https://quant.stackexchange.com/a/70048 You are on the right track. The value of an auto callable bond is always greater than the issuer callable bond, whatever the specified level of the autocalls. If you vary the auto call level, you will get some optimal value (by which I mean that the value is minimized) or more precisely an optimal vector of autocalls by date. However this optimal value will still be higher than the issuer callable bond. The proof of this is straightforward (at least in the greater than or equal sense) since the issuer can always preselect a fixed call decision. In practice , the value of an auto call is strictly greater , because the optimal exercise decision is path dependent, and is dependent on the evolution of several variables such as the yield level of various maturity bonds by the same issuer , and on interest rate and credit volatility. More advanced models such as Longstaff Schwartz have been developed to take account of these variables as determinants of optimal exercise policy, but those models are still strictly an overestimate of the bond value relative to the full issuer call.
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