Valuing a Bond with Same-Date Call and Put Options

Summary

The document considers a bond with a call and a put exercisable on the same date, using different strikes to illustrate how the embedded options affect value. Under its stated assumptions—a forward bond price of 100 and no discounting—the example values the underlying bond at 100, subtracts the call payoff at a strike of 20, and adds the put payoff at a strike of 150. The resulting combined value is 70.

The calculation treats both option payoffs as applying simultaneously, rather than choosing an exercise order. It is a simple payoff illustration, not a complete valuation framework: it omits discounting, market conventions, exercise rights and priorities, and any contractual rules governing simultaneous exercise. In practice, the bond documentation and product structure determine whether these payoffs can coexist and how they are settled. The example therefore clarifies arithmetic under its assumptions but does not establish a universal convention for callable and puttable bonds.

Key ideas

• A bond with embedded options can be decomposed into the underlying bond and option payoffs.
• The example subtracts the call payoff and adds the put payoff to the bond value.
• Its result assumes a forward value of 100 and no discounting.
• Whether both rights apply together depends on the instrument's contractual terms.

Tags

# Bond with embedded call and put on the same date


# Bond with embedded call and put on the same date












Theoretically callable/puttable bond can have call option and put option on the very same date. Usually they have the same strike and that strike is 100, but let's say the C/P bond has put at 150 and call at 20.

Assuming the forward price is 100 and no discounting takes place, how is this resolved? Should I ask the user to specify the order? Should I value both simultaneously?





- Both:

- Bond = 100

- -Call = -max(100-20, 0) = -80

- Put = max(150-100, 0) = 50

- C/P Bond = 100-80+50 = 70

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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