Timeline for What is market standard model in equity, FX and interest rates exotics?
Current License: CC BY-SA 4.0
23 events
| when toggle format | what | by | license | comment | |
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| Mar 23, 2019 at 10:51 | vote | accept | opt | ||
| Mar 15, 2019 at 13:44 | comment | added | opt | Thanks. I opened a new question: quant.stackexchange.com/questions/44580/… | |
| Mar 15, 2019 at 6:09 | comment | added | user34971 | The comment thread is becoming rather long. Maybe you should create a new question if there are further specifics you'd like to know. | |
| Mar 15, 2019 at 6:08 | comment | added | user34971 | In practice, the Heston model with or without time dependent parameters, is calibrated to all available quoted options by minimizing the distance of the model options prices to quoted options prices. Hope this clarifies. | |
| Mar 15, 2019 at 6:07 | comment | added | user34971 | The Heston model has 5 parameters: the current instantaneous volatility, the mean reversion speed, the long term mean, the vol of vol, and correlation. So you need 5 options of different strikes and but not necessarily different maturities (although that would be recommended) to calibrate the Heston model to the whole surface. If the parameters were time dependent then you'd need 1 option for the instaneous vol calibration, and 4 per maturity for the remaining time dependent parameters. | |
| Mar 14, 2019 at 17:06 | comment | added | opt | But then how can Heston or SABR be applied to FX where only 3 points are quoted? Maybe for SABR it could still work of you impose a value for beta and only calibrate for the remaining 3 parameters, but how can Heston be so popular in FX if only 3 points are quoted for each expiry? | |
| Mar 14, 2019 at 9:39 | comment | added | user34971 | To your last question: well, if pure SV model then in theory you only need as many options as the parameters of the model. Local volatility (and hence LSV) can be seen as a model with an infinite number of parameters in some sense, hence there you need all the points, and therefore need to smooth the surface. | |
| Mar 14, 2019 at 9:37 | comment | added | user34971 | By the way, you might want to look at Jherek Healy's book "Applied Quantitative Finance for Equity Derivatives" and also Peter Austing's book "Smile Pricing Explained". There are some good implementation and theory discussions in both, with Healy's leaning more towards implementation and Austing's towards exposition and theory. Of course these book is for Equity and FX derivs mainly. I am not a rates expert and will leave it to other members to suggest works on rates | |
| Mar 14, 2019 at 9:34 | comment | added | opt | So let's say that I am using FX quotes that only have 3 points (ATM and 25 Delta call/put). If I want to calibrate a SV model like Heston or SABR I first need to apply SVI then on the resulting smile I calibrate the SV model? | |
| Mar 14, 2019 at 9:31 | comment | added | user34971 | Whether you do LSV, SV or LV, you'll need enough strikes to be able to smooth the implied volatility surface as you'll need to be able to numerically differentiate the surface / vanilla options prices. A smooth IV surface is the basis. So the method by which you smooth the surface, e.g. SVI or using Fengler's method, will tell you how many strikes per maturity. For SVI that would be 5 per maturity for example. Also, in the wings in particular you should only look at strikes for which there are non-stale bids in the market. | |
| Mar 13, 2019 at 20:25 | comment | added | opt | In practice how many strikes are needed to fit a LSV model to FX smiles? And how about LV and SV? | |
| Mar 11, 2019 at 22:47 | vote | accept | opt | ||
| Mar 23, 2019 at 10:51 | |||||
| Mar 11, 2019 at 11:19 | comment | added | user34971 | Yes that's correct. MC or PDE depending on the type of derivative. For Greeks you could do bump and revalue or pathwise derivatives, or adjoint differentiation etc. | |
| Mar 10, 2019 at 21:01 | comment | added | opt | So if I want some more general approach it is better to use LSV that can work for any derivative? In summary once you have the LSV parameters calibrated, you need to use a MC simulation of the LSV stochastic processes (one for underlying and one for volatility) to get simulated paths and find a price. I guess the same logic would apply to Greeks as well, but in this case repeating the pricing 2 times to get the base price and the price with shocked parameter (for example volatility if I need Vega)? | |
| Mar 8, 2019 at 9:06 | comment | added | user34971 | Well for very few light exotics, such as the digital, you can do this. But for many other exotics you can't and you really need to do the PDE/MC after calibration of your LSV model. But if all you need is an indicative price then there are 'hacks' to the Black-Scholes model to incorporate stochastic volatility corrections. Google for example "vanna-volga" methods for barrier options in FX. | |
| Mar 8, 2019 at 8:39 | comment | added | opt | So for these exotics all you have to do is to interpolate the current smile with some model (not necessarily LSV) and compute the skew correction on top of the Black Scholes price of the exotics? So, in a way, Black Scholes plus a model to interpolate the smile is still standard approach to most easy to price exotics? | |
| Mar 8, 2019 at 8:08 | comment | added | user34971 | Assuming there is a market implied volatility smile (ie vanilla options are traded), then for some light exotics such as digitals, even though you don't have the model closed form solution you can relate the price to the Black-Scholes price. Eg a digital is basically an infinitely tight call spread, so you can relate it to the Black-Scholes price of a digital plus a skew correction. But for general exotics you cannot even do this. The same goes for Greeks. | |
| Mar 7, 2019 at 15:03 | comment | added | opt | This is interesting. So the only closed formula for exotics like barriers or digitals is the Black Scholes? If we want to use more realistic models like SABR or LSV then we can only simulate the corresponding processes with MC and get the price? The same logic would apply to the corresponding Greeks I assume? | |
| Mar 7, 2019 at 12:25 | comment | added | user34971 | SABR has a closed form for pricing vanilla options. Actually it's not even the exact solution, but a (very good) approximation for the implied volatility for vanilla options if the underyling dynamics were indeed SABR. You'd still Monte Carlo or PDE methods for exotics. Same goes for LMM, which is complicated by the fact that you'd probably like a correlation structure for the different Libor rates. For LSV I am not aware of any closed form expression for vanillas even. There you'd have to use PDE r MC methods even for vanilla options. | |
| Mar 6, 2019 at 21:37 | comment | added | opt | Thanks. I saw that SABR has closed form solution for pricing options. How about LSV and Libor Market Model? Do they come with closed form solution or the pricing is via Monte Carlo simulation? | |
| Mar 5, 2019 at 21:14 | comment | added | FunnyBuzer | I'd say that for exotic IR derivatives, the Libor market model is the standard. | |
| Mar 5, 2019 at 17:19 | comment | added | opt | SABR also for exotics rates derivatives? | |
| Mar 5, 2019 at 16:02 | history | answered | user34971 | CC BY-SA 4.0 |