Interview Question

[viv_d]

I recently went through an interview for a grad program, with a background in CS, I didn't do well answering some of the questions, can some one help?

1. Why is risk free rate used in BS model?
2. How can you use a quantitative way to model the value of S&P stock index in two weeks?

Thank you so much!

 

[kuwantfin]

1. because we want to model the option price for a risk neutral investor. For risk neutral investor, the expected return is risk free rate.
2. in simple words, the discounted value of expected payoff of S&P and expected payoff could be calculated based on multiple scenarios of S&P (on base level MC could be used)

 

[Jeffrey K.W. Lo]

My answers if I was asked these questions:

1) RFR differs between companies and depends on your purpose when pricing with the model. For example, if you can borrow unlimited funds at 1% then it'd make sense to invest into all arb opportunities that yields 1.1% or more.
2) brownian motion using historical or forecasted vol?

Jeffrey

 

[ValueSeeker]

The answer for the first question is because of a "change of measure" from the mean of an asset (which no-one knows for sure) to a measure that is risk-neutral (you can use a return everyone knows, the risk free rate). By changing measures, the mean return won't matter.
Question 2: You can't predict the S&P but you can price a derivative based on the S&P being the underlying. You can model the S&P using a diffusion model which is simply d(S&P)/S&P = rf * dt + sigma * dz . z is a Brownian motion (a normal(0, T)).