Derivatives: option pricing help

Have some questions, please help

1.) When calculating the value of an option using a binomial model (say a european call option on a bond), we essentially discount the futue payoffs/intrinsic values to find the option price. However, when valuing an otherwise identical american option the text says to use the higher of either the option value of the intrinsic value.

My question: how can the intrinsic value be higher than the option value? I didn’t think this could be the case bc the option includes time value which intrinsic value does not. Unless this is merely highlighting that the option value for an american option can be higher bc it is exercisable (which of course makes american options more valuable than euros). So in this case, the intrinsic value is the actual value of the american option which is not equal to the Euro option.

2.) How is time value captured using the binomial model if we’re discounting the intrinsic value at expiration ?? Is it bc the prices at that point reflect the future volatility and thus the time value is inherent in the intrisic value/payoff at expiration?

3.) Can someone help me better understand this concept, from the text: “in the binomial model, the hedge portfolio is riskless over the next period, and the no-arbitrage option price is the one that guarantees that the hedge portfolio will yield the Rf rate”.

Thanks, all !!!

You should reference what section you read this from. It would depend if you’re valuing a call option on a bond or if your valuing a bond with an embedded call option. A bond with an embedded call would be worth less than an option free bond.

You’re discounting the probability weighted avg of each node. So with a european call option we would be discounting the probability weighted average of the two cashflows from each node at expiration where the option is exercised. The intrinsic value of a call or put at expiration is equal to its profit, because there is no chance of future price change.

Which reading is this from? Haven’t read this yet but I’ll take a look. But I think, overall you should go back and take a look at pg 267 of Fixed Income - Valuing a bond with an Embedded Call Option. This section covers using the Binomial model to value Embedded options and I thought it covered it pretty well.

Yes, can you advise where you got this from, particularly the last line?

It’s actually from Schweser on page 75 at the start of the black-shoals discussion regarding the assumptions underlying the Black-shoals model. It’s regarding the fact that the black-shoals model is derived from the same no-arbitrage assumption used to value options with a binomial model. Just don’t understand the undlying talk of “hedge portfolios” .

This might be helpful if you’re financially literate.

The basic idea is that you can use the binomial model to achieve a general solution in terms of the option price, and the no-arbitrage price for the option is the one where your payoff is higher by exact amount of simply investing at the risk-free rate.