Boa Quant Pricing Internship Tech Phone Screen Interview Questions Part 2

Q5. Assuming there are six-month and three-month europaeus calls, same strike, same expiry, what difference should be shown on the graph? A: I started rambling, saying it's because of the optionless c

Q5. Assuming there are six-month and three-month europaeus calls, same strike, same expiry, what difference should be shown on the graph? A: I started rambling, saying it's because of the optionless certainty of 3m, and from the Black-Scholes relationship, we can see that the smaller T is, the smaller the option value should be. (I've attached the graph I drew.) Then I talked about the relationship between intrinsic value and time value of option. I said that there's a greater probability that the underlying price will rise more than K in six months. Q6. Draw a graph of delta, and ask how to determine the range of delta? (Finally, something a little more comfortable!) A: The graph is just what I remembered. My immediate thought was to differentiate with respect to Black-Scholes, and then I remembered that it was derived as N(d1) in class, so I just said the normal CDF, and that d in the CDF depends on T. I explained why the delta of 3m is larger than the delta of 6m? The range is simple: rate of change, between 0 and 1. This explains how changes in the underlying asset's unit change affect the option's value; 0 indicates no effect, and 1 indicates a 1:1 ratio. Q7. Draw Gamma. A: Basically the same as above, draw a graph and explain. However, the explanation might not have been thorough enough. I mentioned "in the money" and "out the money" here, but upon reflection, it seems irrelevant.