Hi
I have a general question that I've not been able to figure out.
vol<-.1
strike<-1.
library(RQuantLib)
EU<-EuropeanOption(type="call",underlying=1.,strike=strike,dividendYield=0.,riskFreeRate=.02,maturity=1.,
volatility=vol)
print(EU)
Concise summary of valuation for EuropeanOption
value delta gamma vega theta rho divRho
0.0502 0.5987 3.8667 0.3867 -0.0303 0.5485 -0.5987
stocks<-exp(rnorm(10000, mean=.02-vol^2/2, sd=vol))
callvals<-pmax(0.,stocks-strike)
summary(exp(-.02)*callvals)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.00000 0.00000 0.01329 0.04987 0.08314 0.47050
So that's all as expected, the mean discounted call value under the
risk-neutral measure and the BS price are close.
However we are told that the option price doesn't depend on the mu of
the stock, and there are stocks which have consistently higher mu's
(BRK, GOOG) than other stocks (YHOO) for a similar level of vol. So
let's say I have a high-mu stock:
mustocks<-exp(rnorm(10000, mean=.15, sd=vol))
mucallvals<-pmax(0.,mustocks-strike)
print(summary(mustocks))
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.8155 1.0850 1.1630 1.1680 1.2440 1.7400
print(summary(exp(-.02)*mucallvals))
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.00000 0.08153 0.15670 0.16590 0.23860 0.73860
so i can buy this call for the BS price of $.05, which equals its
discounted payoff in RN, but now on this high-mu underlying i get a mean
discounted value of .165, ie. 200% mean roi, with the lower quartile
giving a paltry 60% return.
what am i doing wrong?
thanks!
-neal
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