From Local Volatility to Local L¶evy Models
نویسندگان
چکیده
We de ̄ne the class of local L¶evy processes. These are L¶evy processes time changed by an inhomogeneous local speed function. The local speed function is a deterministic function of time and the level of the process itself. We show how to reverse engineer the local speed function from traded option prices of all strikes and maturities. The local L¶evy processes generalize the class of local volatility models. Closed forms for local speed functions for a variety of cases are also presented. Numerical methods for recovery are also described.
منابع مشابه
Evy - Driven and Fractionally Integrated Armaprocesses with Continuous Time Parameterpeter
The deenition and properties of L evy-driven CARMA (continuous-time ARMA) processes are reviewed. Gaussian CARMA processes are special cases in which the driving L evy process is Brownian motion. The use of more general L evy processes permits the speciication of CARMA processes with a wide variety of marginal distributions which may be asymmetric and heavier tailed than Gaus-sian. Non-negative...
متن کاملEvy Driven and Fractionally Integrated Arma Processes with Continuous Time Parameter
The de nition and properties of L evy driven CARMA continuous time ARMA processes are re viewed Gaussian CARMA processes are special cases in which the driving L evy process is Brownian motion The use of more general L evy processes permits the speci cation of CARMA processes with a wide variety of marginal distributions which may be asymmetric and heavier tailed than Gaus sian Non negative CAR...
متن کاملAbrupt Changes in Volatility: Evidence from TEPIX Index in Tehran Stock Exchange
In this paper, we have examined abrupt changes in volatility of TEPIX index in Tehran stock exchange during August 23, 2010 to June 12, 2014. Applying the iterated cumulative sum of squares (ICSS) algorithm proposed by Inclan and Tiao (1994) and the modified version of this algorithm consisting Kappa 1 and Kappa 2 test statistics developed by Sansó et al. (2004), we have specified that the dete...
متن کاملRight Inverses of L Evy Processes and Stationary Stopped Local Times
If X is a symmetric L evy process on the line, then there exists a non{decreasing, c adl ag process H such that X(H(x)) = x for all x 0 if and only if X is recurrent and has a non{trivialGaussian component. The minimal such H is a subordinatorK. The law of K is identi ed and shown to be the same as that of a linear time change of the inverse local time at 0 of X. When X is Brownian motion,K is ...
متن کاملStochastic Volatility for L¶evy Processes
Three processes re°ecting persistence of volatility are formulated by evaluating three L¶evy processes at a time change given by the integral of a square root process. A positive stock price process is then obtained by exponentiating and mean correcting these processes, or alternatively by stochastically exponentiating the processes. The characteristic functions for the log price can be used to...
متن کامل