Christian Fries
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 Jul21 comment How to calculate return rates with negative prices? Black-Scholes seems to be not adequate. A displaced model may be more adequate. Of course, you may calculate an implied BS vol. What is your heeding strategy? What does your hedge do if prices are negative? The answers to these question should give the you the option prices. Not the blind believe in an inappropriate model... Jul21 comment How to calculate return rates with negative prices? Is P the price or the return? Jul21 comment How to calculate return rates with negative prices? If $P_{i}/P_{i-1} < 0$, then the assumption of log-normality is clearly wrong. You should consider an alternative model. Why do you think that absolute changes are not suitable? Why do you believe in log-normality so strongly? You may also consider a displaced log-normal model, like in the cited paper. If data with $P_{i}/P_{i-1} < 0$ is just a rare sample error, you may consider leaving that data out. Put it appears as if this is not the right way here... Jul21 comment How to calculate return rates with negative prices? @Joao Serafim: This does not solve the explosion for $P_{i-1}$ becoming close to zero. You won't consider wiggeling around zero as such a huge vol, or do you? Jul21 comment How to calculate return rates with negative prices? @Hebe: Which does not work if P(i-1) is zero. Actually (P(i)/P(i-1))-1 is just a finite difference approximation of the log-return. Jul21 revised How to calculate return rates with negative prices? Texed it Jul21 answered How to calculate return rates with negative prices? Jul13 answered The reason behind the selection of a 1 standard deviation movement for self financing delta hedge Jun29 comment expected value of the discounted payoff This is a statement. What is the question? Jun29 answered Stock prices using a monte carlo simulation with a normal inverse gauss distribution Jun17 comment Malliavin Calculus I would suggest splitting this into two separate questions: one on Malliavin Calculus and one on Multi-Fractals Models. I could then maybe provide some comments on Malliavin Calculus: looking at the "proxy simulation scheme" technique can be useful, since it is a "discrete analog" (on the level of the discretization scheme, like Eurler scheme) of what Malliavin calculus does in the continuous setup. Jun10 comment Is the price of European put option monotone in volatility if we replace BM in Black-Scholes with a general Levy process? What is the definition of "volatility" if you consider a general Levy process? If you define it as the implied volatility of the (respective) put option: then yes. It is trivial. The price is a monotone function of the implied Black volatlity. May27 revised Matlab; How to specify Coupon frequency for Interest Rate Swap added 126 characters in body May27 answered Matlab; How to specify Coupon frequency for Interest Rate Swap May16 revised How to use Itô's formula to deduce that a stochastic process is a martingale? added 55 characters in body May16 revised How to use Itô's formula to deduce that a stochastic process is a martingale? added 55 characters in body May16 answered How to use Itô's formula to deduce that a stochastic process is a martingale? May13 revised Quadratic variation question added 198 characters in body May13 comment Quadratic variation question Ito actually tells you that $d(B^2) = BdB + BdB + dt$. So ii) might mean: Proof it using Ito, while iii) means proof it in an elemantary by repeating the proof of Ito for the special case of $B^2$. May11 revised how to derive yield curve from interest rate swap? added 1 characters in body