Simulation Engines

ravishankar80

New Member
Hi David,

I may have missed out on lognormal and jump-diffusions but I wanted to understand the difference and when they are applied.
-For foreign exchange rates in major currency we use lognormal and for emerging currency jump-diffusions.
-Interest rates in developing economies: normal (low rates) or lognormal distribution (high rates)
-Equities: lognormal (high liquidity) or jump-diffusion (low liquidity)

What determines usage of lognormal,normal and jump-diffusion ? I see a very brief explanation of lognormal as it is not a part of the AIM

Thanks

Ravi
 

David Harper CFA FRM

David Harper CFA FRM
Subscriber
Hi Ravi,

These generalities are from Canabarro & Duffie on counterparty risk. There are tendencies or typical practices, they are not absolutes. I regret this inclusion in 2008 FRM b/c we do not explore any of it really. IMO, there isn't much of a middle ground btwn (i) memorize the list or (ii) take a plunge into deep pool of stochastic process. In brief, any brief answer will be too glib to give this area justice (IMO). And, further, i am somewhat familiar with equities/interest rates but not currencies (and i am not expert in any of them, i have customers who well surpass me on this specialty area. The more i learn about stochastic processes, the less i know!). So, i'd offer:

* Our "baseline" is arguably, as an introduction to quant fiance, the geometric Brownian Motion (GBM, subclass of Weiner) that underlies the (basic) Black-Scholes we see in Hull. This GBM is indeed a lognormal diffussion. Lognormal: returns [=LN (s1/s0)] are normal, such that prices are lognormal. Diffusion: the are smooth/continuous over time as opposed to having discrete/abrupt steps. There is more here on normal/lognormal diffusion.

* You'll note the jump or jump-diffusion naturally enters for low-liquidity situations. Hopefully this is intuitive. Low liquidity implies the prospect of abrupt/discrete changes.

* I wouldn't take Canabarro's generalities too seriously; in the case of interest rates, there are several classes of diffusion and jump-diffusion models. I am not even sure i'd agree with their characterization, here. But it doesn't matter, they are simply saying, really, that different instruments in different markets will be characterized by different stochastic processes. The great team at fixedincomerisk.com devoted their second book (a masterpiece) to this.


David
 
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