APPENDIX TO CHAPTER 16Fixed Income Options
A16.1 THEORETICAL FOUNDATIONS FOR APPLYING BLACK‐SCHOLES‐MERTON (BSM) TO SELECTED FIXED INCOME OPTIONS
The justification for applying BSM in each of the cases of the text takes the following form:
- Given the functional form of a probability distribution (e.g., normal, lognormal), there exist parameters of that distribution such that
, the arbitrage‐free price of any asset today, is given by,
where 
is the price at time 
of an asset chosen as the numeraire; 
is value at time 
of an asset being priced today, including reinvested cash flows; and 
gives expectations as of time 
under the appropriately parameterized probability distribution. Equation ...
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