Belated R.I.P. Stanislaw Petrow (May 19, 2017). The international news media only found out today that Petrow has died. RIP. His contribution will be judged by history. Petrov, Stanislav Evgrafovich [ltr] September 26, 1983 [ edit ] edit wiki-text ] On the night of September 26, 1983, Lieutena...
There is only one way to present Heston's equation (BSE U ). This is to present BS portfolio in which an option is hedged by underlying security. Heston reference on " standard arbitrage arguments B&S&M for any asset U ( S , v , t ) must satisfy (BSE U ) " is a way to hide deri...
In his paper it was assumed that [$] d S ( t ) = \mu S ( t ) \,dt + \sqrt { v ( t )} S ( t ) \,dw_1 ( t ) [$] (1) [$]d v ( t ) = k [ \theta - v ( t ) ] \,dt + \sigma\sqrt { v ( t ) } \,dw_2 ( t ) [$] (2) It was stated that "standard arbitrage arguments (B&S&M) demonstrate that value o...
The Heston start point is the eq (6) [$]\frac{1}{2} v S^2 \frac {\partial^2{U}}{\partial { S^2}} + \rho \sigma v S \frac{ \partial^2 {U}}{\partial U \partial v} + ... + [ k ( \theta - \lambda ( S , v , t ) ] \frac{ \partial U}{\partial v } - r U + \frac { \partial U}{\partial t} \,=\,0 ...
In his paper it was assumed that [$] d S ( t ) = \mu S ( t ) \,dt + \sqrt { v ( t )} S ( t ) \,dw_1 ( t ) [$] (1) [$]d v ( t ) = k [ \theta - v ( t ) ] \,dt + \sigma\sqrt { v ( t ) } \,dw_2 ( t ) [$] (2) It was stated that "standard arbitrage arguments (B&S&M) demonstrate that value o...
In his paper it was assumed that [$] d S ( t ) = \mu S ( t ) \,dt + \sqrt { v ( t )} S ( t ) \,dw_1 ( t ) [$] (1) [$]d v ( t ) = k [ \theta - v ( t ) ] \,dt + \sigma\sqrt { v ( t ) } \,dw_2 ( t ) [$] (2) It was stated that "standard arbitrage arguments (B&S&M) demonstrate that value of...
Having math - statistics edu it might be reasonable first to look at https://en.wikipedia.org/wiki/Generalized_method_of_moments. Actually the basis of estimation parameters is its closeness to observed data.To refresh your knowledge you can look at some simple statistics handbook how one estimate ...
I have a good math/stats background, but whenever I try to pick up something on GMM I get lost. Mostly, I struggle with the leaps in mathematical logic between steps in the original paper and others. Are there other subjects I can read up on to prepare for another stab at GMM? Or is there some lite...
There is no low which specifies application of the notion closed form. It is not common to say closed form of a number [$]\pi , \sqrt 3[$] or others. In finance we use closed form formula though ib math in a similar situation we say analytic, exact, explicit formula or solution. When I first read ex...
Yes, eg if we have the equation A = pi r^2 then we can't compute it exactly for most r. If the answer of a problem is represented in the form [$]\pi r^2[$] then it is the closed form solution. You need an algorithm or series expansion to compute pi. Iifinite time to fill it. And that's just the sta...
So, from these examples can we conclude that closed-form solution break down for certain values of the input parameters, e.g. Schroder's CEV option formula converges slowly for [$]\beta = 1[$]. Compare the CEV PDE equivalent that evolves gracefully to the BS PDE when [$]\beta \rightarrow 1[$]. Whe...
I think we can simply imagine that at the time when Bessel functions was introduced it was difficult to accept that representation of a solution of a particular problem by using Bessel functions could be called a closed form representation. Today when Bessel functions are well known in theoretical ...
I think we can simply imagine that at the time when Bessel functions was introduced it was difficult to accept that representation of a solution of a particular problem by using Bessel functions could be called a closed form representation. Today when Bessel functions are well known in theoretical a...