I'm still struggling with the fact that the expected return on the stock is 3.24% (implying a stock value of $51.62 at expiry) and the option values predicted by the model converge to $3.20 and $1.60. These option values do not make sense. I think it may be because the model is using stock RETURNS to predict option PRICES. Returns are normally distributed while prices are not. Think of the bell curve; for returns it is symmetrical as the values can be positive or negative. But prices cannot be negative, their lower bound is zero. So, when the options are valued by taking the average of all their predicted prices, the result is overstated because the model is not properly accounting for negative returns. I think this is a flaw in the model because, intuitively, the option values just do not make any sense. How can a call and a put with $50 strikes be valued at $3.20 and $1.60 respectively when the expected value of the stock at expiration is $51.6 (3.24% return)? How does one interpret such option prices given the model's inputs?
Excellent video. Thank you for the detailed example. I replicated your example and the values i got for the call and the put options at expiration seemed to converge on 3.2 and 1.6 respectively. But an average stock return of 3.24% would imply a stock value of 51.62 at expiration and therefore a call value of 1.62 and a put value of 0 - on average. What don't I understand? Also, how do we interpret the call and put values generated by Monte Carlo? Are these the "expected values" for the options given the stock average return and standard deviation? Thanks.
I'm still struggling with the fact that the expected return on the stock is 3.24% (implying a stock value of $51.62 at expiry) and the option values predicted by the model converge to $3.20 and $1.60. These option values do not make sense. I think it may be because the model is using stock RETURNS to predict option PRICES. Returns are normally distributed while prices are not. Think of the bell curve; for returns it is symmetrical as the values can be positive or negative. But prices cannot be negative, their lower bound is zero. So, when the options are valued by taking the average of all their predicted prices, the result is overstated because the model is not properly accounting for negative returns. I think this is a flaw in the model because, intuitively, the option values just do not make any sense. How can a call and a put with $50 strikes be valued at $3.20 and $1.60 respectively when the expected value of the stock at expiration is $51.6 (3.24% return)? How does one interpret such option prices given the model's inputs?
Excellent video. Thank you for the detailed example. I replicated your example and the values i got for the call and the put options at expiration seemed to converge on 3.2 and 1.6 respectively. But an average stock return of 3.24% would imply a stock value of 51.62 at expiration and therefore a call value of 1.62 and a put value of 0 - on average. What don't I understand? Also, how do we interpret the call and put values generated by Monte Carlo? Are these the "expected values" for the options given the stock average return and standard deviation? Thanks.