Questions tagged [volatility-smile]

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6
votes
4answers
2k views

Downward sloping smile in normal model

We consider an stock price $S$ following a normal model: $dS_t = \sigma dW_t$ We can write this as $\frac{dS_t}{S_t}=\frac{\sigma}{S_t}dW_t$ Hence we can see that $S$ follows a "log-normal" ...
8
votes
2answers
2k views

Arbitrage Free Volatility Smile

When ATM implied volatility is higher than OTM put and call I believe that the volatility smile is no longer arbitrage free? Why is that? On the other hand, when ATM implied volatility is lower than ...
7
votes
3answers
2k 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 ...
9
votes
4answers
1k views

Why does the volatility smile flatten as maturities increase?

First, I can't find a purely "financial" explanation for this. Also the only mathematical explanation I've found so far was using the large deviations theory, which is quite complex. Is there a ...
4
votes
1answer
2k views

parameters in Heston model and their impact on volatility smile

Consider the Heston model given by the following set of stochastic differential equations: $$\frac{dS_{t}}{S_{t}}=\mu_{t}dt+\sqrt{V_{t}}dW_{t}, S_{0}>0,$$ $$dV_{t}=\kappa(\theta-V_{t})dt+\xi\sqrt{...
8
votes
3answers
2k views

Concave volatility smile

Under what circumstances can implied volatility smile be concave (ATM implied volatility higher than OTM put and call)? I know that a slight concavity is not prohibited by no-arbitrage... What are ...
2
votes
1answer
206 views

LSV model calibration with only few quotes per maturity

At this link I have asked what is the market standard when pricing options in different asset classes. Based on the answers, the standard for FX and equities seems to be the local-stochastic ...
0
votes
1answer
169 views

What is market standard model in equity, FX and interest rates exotics?

Is there any industry consensus about the model to use for pricing exotics in equity, FX and interest rates? I assume that for vanilla options they all use Black model, but how about exotics? Also, ...
7
votes
1answer
4k views

SABR calibration: simple explanation and implementation

I would like to learn more about the SABR model and ho it is used in modeling smiles in equity, FX and rates markets. How would you explain the process and its implementation in simple steps? Any web ...
1
vote
3answers
449 views

At-the-money and volatility smile

In a volatility smile; why is the ATM point usually or ideally at the bottom? In other words, why is the "smile" smile shaped as opposed to another shape?
1
vote
1answer
249 views

On a FX volatility smile, Is a-delta put volatility equal to (1-a)-delta call volatility?

On a FX volatility smile in terms of delta, If I want 95-delta put vol, Is this volatility equal to a 5-delta call vol, and viceversa? Thanks.