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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

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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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  • $\begingroup$ Thanks for your answer and your time to write it. Just a quick one: I think with several call dates this problem of finding the matching autocallable level becomes a multidimensional one, right? Each call date logically refers to one specific autocall level I guess and not just one level for all dates to match the issuercallable bond PV sufficiently? $\endgroup$
    – T123
    Mar 3, 2022 at 7:10
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    $\begingroup$ yes, agree. that's what i meant by an autocall 'vector' $\endgroup$
    – dm63
    Mar 4, 2022 at 13:06
  • $\begingroup$ Thanks a lot, i've already implemented a search algo over the various autocall-levels in our pricing engine... the PV matches nicely $\endgroup$
    – T123
    Mar 4, 2022 at 13:44

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