In the discussion associated with our T5-40 question at old https://forum.bionicturtle.com/threads/l2-t5-40-replicating-callable-bond-tuckman.3551/post-78646 @Sixcarbs asked for a fresh situation (same mechanics but simply with different but coherent numbers). Here is what I've come up with

Assume the following:

Solution here coming soon ...

Assume the following:

- Currently the six-month spot rate,
**S(0.5) = 3.00%**, and one-year spot rate,**S(1.0) = 3.10%** - Our presumed binomial interest rate tree characterizes (short-term)
*six-month rates*and has only two steps, so each step is also six-months and the tree only extends out to one year. At each node, six-month rate jumps up or down**40 basis points**with equal probability. The initial six-month rate is 3.00%. In six months, then, the new six-month rate will either be**3.40% (with 50% probability)**or**2.60% (with 50% probability)**. - We are evaluating a one-year zero-coupon bond with a face value of $1,000 and a
**call option**on this bond with a**strike price of $985.00**; the option matures in six months (like Tuckman's example). - I believe my mechanics match Tuckman's Chapter 7 example, but of course my values are different. For comparison,
- His spot rates are S(0.5) = 5.00% and S(1.0) = 5.15%
- His six-month binomial rate tree starts at 5.00% and jump up/down by 50 bps with equal probability; i.e., to 5.50% or 4.50%
- His bond has a face value of $1,000.00 and his six-month option has a strike price of $975.00

- What is the bond's (theoretical) market price?
- We are told (given) that the real-world (aka, true) probabilities are 50%/50%, but what are the risk-neutral probabilities?
- If we use the real-world probabilities, what is the
*expected discounted value*of the call option? - If we use the risk-neutral probabilities, what is the market price of the call option?
- How can we interpret the risk-neutral probabilities?

Solution here coming soon ...

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