All Questions
Tagged with implied-volatility stochastic-calculus
11 questions
3
votes
1
answer
508
views
Volatility swaps hedging
I have heard that traders use a straddle to hedge volatility swaps (in the FX context), although I could not figure out the specifics. Is this type of hedge used in practice? And if yes, how does it ...
- 757
0
votes
1
answer
460
views
Smile wings and varswap pricing
Is it true that far wings of the volatility smile have an outsized influence on the price of a variance swap? Is there a mathematical argument demonstrating this idea? What do we generally refer as ...
- 757
2
votes
0
answers
186
views
If $\Delta \log(V_{t})$ behaves like the increments of fractional Brownian motion, why do we model the rough volatility as follows
From Gatheral's paper, Volatility is rough and empirical evidence, it is clear that $\big\{\log(V_{t+1})-\log(V_{t})\big\}_{t}$ behaves like the increments of fractional Brownian motion $B^{H}$ with ...
- 93
0
votes
0
answers
46
views
Maximum entropy probability distribution for $S_T$ implied from discrete market quotes
Consider a maturity $T$, for this maturity I have some implied volatility from market denoted $\sigma^{0}_{i}$. I want to interpolate these volatility using Entropy approach, by using $\sigma^{0}_{i}$...
- 863
2
votes
0
answers
206
views
Implied Volatility is the harmonic average of Local Volatility
I am trying to demonstrate the famous result that states that when $T \rightarrow 0$, the Implied Volatility is the harmonic average of Local Volatility.
I am st the final stage, and I have the ...
- 863
6
votes
0
answers
300
views
Closed formula for computing Implied Volatility from Local Volatility function
The main result of this paper (Asymptotics and Calibration in Local Volatility Models, Berestycki, Busca, and Florent. Quantitative Finance, 2002) is equation (16) on page 63, that states that:
In the ...
- 863
1
vote
1
answer
162
views
Calculating Expectation of Stochastic Volatility
I have a question while reading THE NELSON–SIEGEL MODEL OF THE TERM
STRUCTURE OF OPTION IMPLIED VOLATILITY
AND VOLATILITY COMPONENTS by Guo, Han, and Zhao.
I don't understand why the above equations ...
- 11
4
votes
1
answer
668
views
Dependence of implied volatility on spot-vol correlation
I have the following general SV model:
$$
dS = \sigma S dW_S
$$
$$
d\sigma = a(\sigma,t) dt + b (\sigma, t) dW_\sigma
$$
$$
dW_S dW_\sigma = \rho dt
$$
where $a , b$ are deterministic functions of $\...
user34971
14
votes
0
answers
576
views
Jim Gatheral's ansatz
In the Ansatz section of Jim Gatheral's book Volatility Surface (page 32), he assumes $$\mathbb E[x_s|x_T]=x_T\frac{\hat w_s}{\hat w_T}$$
where $\hat w_t:=\int_0^t \hat v_s ds$ is the expected total ...
- 2,876
8
votes
1
answer
4k
views
Implications of shifting the lognormal model for forward rates from a probability perspective
I have a question regarding the application of a shift to the Black-Scholes formula for negative forward rates.
I am reading in the Brigo book that "increasing the shift $\alpha$ shifts the ...
- 483
6
votes
1
answer
323
views
Derivation of the Stochastic Vol PDE
I'm trying to follow the derivation of the stochastic vol pde for an option price - as given in Gatheral (The vol surface), Wilmott on Quant Finance and many other places. As usual one starts off with ...
- 205