12 questions linked to/from Variance replication using options
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### Replication of variance swap using vanilla option under black and scholes model with nonzero risk-free rate and nonzero dividend [duplicate]

I didn't find the formula for the following portfolio (variance swap replication) with nonzero risk-free rate and nonzero dividend under black and scholes model : I found formula and proof only with ... 12k views

Really new to financial Maths. I am currently having problems with the Carr-Madan Formula. $$f(S_T)=f(F_t) + f'(F_t) (S_T - F_t) + \int_0^{F_t} f''(K) (K-S_T)^+ \ d K + \int_{F_t}^{\infty} f''(K)... 10 votes 3 answers 11k views ### Forward implied volatility Can one price accurately by only using vanilla options a derivative that is exposed/sensitive mainly to the forward volatility ? If it is impossible, why do we hear sometimes "being long a long ... 10 votes 3 answers 5k views ### Why is a variance swap long skew? I can appreciate the mathematical derivation, but can anyone explain this in a more intuitive sense? I often come across the mistaken belief that due to the replicating portfolio being long more ... 9 votes 3 answers 760 views ### Construction of VIX and VVIX I just read the CBOE's Whitepapers for VIX and VVIX and notice that they are constructed in the same way, i.e. a range of calls and puts on the respective underlyings (S&P500 in case of VIX, and ... 4 votes 1 answer 1k views ### Intuition for the Effect of Vol of Vol in Heston Model on Volatility Surface I was hoping someone could describe the economic/mathematical intuition behind the effect that the vol of vol parameter has on the volatility surface, in particular the slope to maturity. Take for ... 5 votes 3 answers 987 views ### How to hedge a derivative that pays the reciprocal of the stock price? 1) Suppose S is the stock price, how to hedge a derivative that pays 1/S_t at time t? 2) Suppose there will be a dividend of amount d between t and T, how to hedge a derivative that pays ... -2 votes 1 answer 1k views ### How would you price an option with payout ln(St) where St is the stock price at time t I know it has to be done through martingales, but I am not fully sure how to do this BSM pricing. 2 votes 1 answer 1k views ### How to approximate the Carr-Madan decomposition formula? I have came across the excellent answer. I'm looking for a dicrete approximation of the Carr-Madan decomposition formula of the function f(F_T) of the terminal futures price by taking a static ... 2 votes 1 answer 1k views ### Carr-Madan european contingent claim payoff decomposition formula - application Looking for some clarification to the values of the parameters used in the Carr-Madan payoff decomposition formula.$$f(S_T)=f(\kappa) + f'(\kappa) (S_T - \kappa) + \int_0^{\kappa} f''(K) (K-S_T)^+ ...
I am having trouble filling in a few steps in the derivation. From Martin (2017), we get the following assumptions: Constant continuously compounded rate $r$; The underlying doesn't pay dividens; ...
As far as I understand, Variance Swap (VS for short) function as follows : no payment when entering the contract at maturity the VS buyer pays a strike $K^2$ and is paid (by the VS seller) the ...