Linked Questions
12 questions linked to/from Variance replication using options
0
votes
1
answer
284
views
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 ...
user44204
21
votes
3
answers
12k
views
Carr-Madan Formula
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)...
- 211
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 ...
- 436
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 ...
- 101
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 ...
- 93
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 ...
- 344
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 $...
- 51
-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 ...
- 239
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)^+ ...
- 701
2
votes
1
answer
681
views
Deriving the VIX formula
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;
...
- 2,416
3
votes
0
answers
282
views
Variance swap "fast" models
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 ...
- 1,223