Black-Scholes model shares common intuitions with risk-neutral option pricing mo
ID: 2801067 • Letter: B
Question
Black-Scholes model shares common intuitions with risk-neutral option pricing model (also known as the binomial option pricing model). One of the biggest underlying assumptions of risk-neutral (binomial) model is that we live in a risk-neutral world. In a risk-neutral world, all investors only demand a risk-free return on all assets. Although the risk-neutral assumption is counterfactual, it is brilliant and desirable because the risk-neutral assumption doesn’t affect the prices of an option. In another word, prices of an option are exactly the same with or without the risk-neutral assumption. Use your words to explain why that is the case, and how risk-neutral assumption greatly simplifies the calculations of risk-neutral option pricing approach.
Explanation / Answer
Black Scholes model is used to calculate a theoretical price ( ignoring dividends paid during the life of the option) using five key determinants of an options price namely stock price, strike price, volatility, time to expiration, risk free interest rate.
whereas Risk neutral option pricing approach or Binomial model breaks down the time to expiration into Potentially a very large number of time intervals or steps.
With the Binomial model it is possible to check at every point in an option's life ( i,e at every step of the binomial tree) for the possibility of early exercise .
Hence the risk-neutral assumption greatly simplifies the calculations of risk-neutral option pricing approach..
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