ترغب بنشر مسار تعليمي؟ اضغط هنا

Sample path generation of the stochastic volatility CGMY process and its application to path-dependent option pricing

124   0   0.0 ( 0 )
 نشر من قبل Young Shin Kim
 تاريخ النشر 2021
  مجال البحث مالية
والبحث باللغة English
 تأليف Young Shin Kim




اسأل ChatGPT حول البحث

This paper proposes the sample path generation method for the stochastic volatility version of CGMY process. We present the Monte-Carlo method for European and American option pricing with the sample path generation and calibrate model parameters to the American style S&P 100 index options market, using the least square regression method. Moreover, we discuss path-dependent options such as Asian and Barrier options.



قيم البحث

اقرأ أيضاً

88 - Fabien Le Floch 2020
This note shows that the cosine expansion based on the Vieta formula is equivalent to a discretization of the Parseval identity. We then evaluate the use of simple direct algorithms to compute the Shannon coefficients for the payoff. Finally, we expl ore the efficiency of a Filon quadrature instead of the Vieta formula for the coefficients related to the probability density function.
415 - Alexandre F. Roch 2008
In this paper, we study the valuation of American type derivatives in the stochastic volatility model of Barndorff-Nielsen and Shephard (2001). We characterize the value of such derivatives as the unique viscosity solution of an integral-partial diff erential equation when the payoff function satisfies a Lipschitz condition.
We propose a general, very fast method to quickly approximate the solution of a parabolic Partial Differential Equation (PDEs) with explicit formulas. Our method also provides equaly fast approximations of the derivatives of the solution, which is a challenge for many other methods. Our approach is based on a computable series expansion in terms of a small parameter. As an example, we treat in detail the important case of the SABR PDE for $beta = 1$, namely $partial_{tau}u = sigma^2 big [ frac{1}{2} (partial^2_xu - partial_xu) + u rho partial_xpartial_sigma u + frac{1}{2} u^2 partial^2_sigma u , big ] + kappa (theta - sigma) partial_sigma$, by choosing $ u$ as small parameter. This yields $u = u_0 + u u_1 + u^2 u_2 + ldots$, with $u_j$ independent of $ u$. The terms $u_j$ are explicitly computable, which is also a challenge for many other, related methods. Truncating this expansion leads to computable approximations of $u$ that are in closed form, and hence can be evaluated very quickly. Most of the other related methods use the time $tau$ as a small parameter. The advantage of our method is that it leads to shorter and hence easier to determine and to generalize formulas. We obtain also an explicit expansion for the implied volatility in the SABR model in terms of $ u$, similar to Hagans formula, but including also the {em mean reverting term.} We provide several numerical tests that show the performance of our method. In particular, we compare our formula to the one due to Hagan. Our results also behave well when used for actual market data and show the mean reverting property of the volatility.
In this paper we investigate price and Greeks computation of a Guaranteed Minimum Withdrawal Benefit (GMWB) Variable Annuity (VA) when both stochastic volatility and stochastic interest rate are considered together in the Heston Hull-White model. We consider a numerical method the solves the dynamic control problem due to the computing of the optimal withdrawal. Moreover, in order to speed up the computation, we employ Gaussian Process Regression (GPR). Starting from observed prices previously computed for some known combinations of model parameters, it is possible to approximate the whole price function on a defined domain. The regression algorithm consists of algorithm training and evaluation. The first step is the most time demanding, but it needs to be performed only once, while the latter is very fast and it requires to be performed only when predicting the target function. The developed method, as well as for the calculation of prices and Greeks, can also be employed to compute the no-arbitrage fee, which is a common practice in the Variable Annuities sector. Numerical experiments show that the accuracy of the values estimated by GPR is high with very low computational cost. Finally, we stress out that the analysis is carried out for a GMWB annuity but it could be generalized to other insurance products.
121 - Ben Boukai 2021
Following Boukai (2021) we present the Generalized Gamma (GG) distribution as a possible RND for modeling European options prices under Hestons (1993) stochastic volatility (SV) model. This distribution is seen as especially useful in situations in w hich the spots price follows a negatively skewed distribution and hence, Black-Scholes based (i.e. the log-normal distribution) modeling is largely inapt. We apply the GG distribution as RND to modeling current market option data on three large market-index ETFs, namely the SPY, IWM and QQQ as well as on the TLT (an ETF that tracks an index of long term US Treasury bonds). The current option chain of each of the three market-index ETFs shows of a pronounced skew of their volatility `smile which indicates a likely distortion in the Black-Scholes modeling of such option data. Reflective of entirely different market expectations, this distortion appears not to exist in the TLT option data. We provide a thorough modeling of the available option data we have on each ETF (with the October 15, 2021 expiration) based on the GG distribution and compared it to the option pricing and RND modeling obtained directly from a well-calibrated Hestons (1993) SV model (both theoretically and empirically, using Monte-Carlo simulations of the spots price). All three market-index ETFs exhibit negatively skewed distributions which are well-matched with those derived under the GG distribution as RND. The inadequacy of the Black-Scholes modeling in such instances which involve negatively skewed distribution is further illustrated by its impact on the hedging factor, delta, and the immediate implications to the retail trader. In contrast, for the TLT ETF, which exhibits no such distortion to the volatility `smile, the three pricing models (i.e. Hestons, Black-Scholes and Generalized Gamma) appear to yield similar results.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا