• Title, Summary, Keyword: jump diffusion

Search Result 35, Processing Time 0.041 seconds

Valuation of Options in Incomplete Markets (불완전시장 하에서의 옵션가격의 결정)

  • Park, Byungwook
    • Journal of the Korean Operations Research and Management Science Society
    • /
    • v.29 no.2
    • /
    • pp.45-57
    • /
    • 2004
  • The purpose of this paper is studying the valuation of option prices in Incomplete markets. A market is said to be incomplete if the given traded assets are insufficient to hedge a contingent claim. This situation occurs, for example, when the underlying stock process follows jump-diffusion processes. Due to the jump part, it is impossible to construct a hedging portfolio with stocks and riskless assets. Contrary to the case of a complete market in which only one equivalent martingale measure exists, there are infinite numbers of equivalent martingale measures in an incomplete market. Our research here is focusing on risk minimizing hedging strategy and its associated minimal martingale measure under the jump-diffusion processes. Based on this risk minimizing hedging strategy, we characterize the dynamics of a risky asset and derive the valuation formula for an option price. The main contribution of this paper is to obtain an analytical formula for a European option price under the jump-diffusion processes using the minimal martingale measure.

Term Structure Estimation Using Official Rate

  • Rhee, Joon Hee;Kim, Yoon Tae
    • Communications for Statistical Applications and Methods
    • /
    • v.10 no.3
    • /
    • pp.655-663
    • /
    • 2003
  • The fundamental tenn structure model is based on the modelling of the short rate. It is well-known that the short rate depends on the interest rate policy of monetary authorities, especially on the official rate. Babbs and Webber(1994) modelled the tenn structure of interest rates using the official rate. They assume that the official rate follows a jump process. This reflects that the official rate infrequently changes. In this paper, we test this official tenn structure model and compare the jump-diffusion model with the pure diffusion model.

EULER-MARUYAMA METHOD FOR SOME NONLINEAR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH JUMP-DIFFUSION

  • Ahmed, Hamdy M.
    • Journal of the Korean Society for Industrial and Applied Mathematics
    • /
    • v.18 no.1
    • /
    • pp.43-50
    • /
    • 2014
  • In this paper we discussed Euler-Maruyama method for stochastic differential equations with jump diffusion. We give a convergence result for Euler-Maruyama where the coefficients of the stochastic differential equation are locally Lipschitz and the pth moments of the exact and numerical solution are bounded for some p > 2.

ASYMPTOTIC RUIN PROBABILITIES IN A GENERALIZED JUMP-DIFFUSION RISK MODEL WITH CONSTANT FORCE OF INTEREST

  • Gao, Qingwu;Bao, Di
    • Journal of the Korean Mathematical Society
    • /
    • v.51 no.4
    • /
    • pp.735-749
    • /
    • 2014
  • This paper studies the asymptotic behavior of the finite-time ruin probability in a jump-diffusion risk model with constant force of interest, upper tail asymptotically independent claims and a general counting arrival process. Particularly, if the claim inter-arrival times follow a certain dependence structure, the obtained result also covers the case of the infinite-time ruin probability.

Valuation of American Option Prices Under the Double Exponential Jump Diffusion Model with a Markov Chain Approximation (이중 지수 점프확산 모형하에서의 마코브 체인을 이용한 아메리칸 옵션 가격 측정)

  • Han, Gyu-Sik
    • Journal of Korean Institute of Industrial Engineers
    • /
    • v.38 no.4
    • /
    • pp.249-253
    • /
    • 2012
  • This paper suggests a numerical method for valuation of American options under the Kou model (double exponential jump diffusion model). The method is based on approximation of underlying asset price using a finite-state, time-homogeneous Markov chain. We examine the effectiveness of the proposed method with simulation results, which are compared with those from the conventional numerical method, the finite difference method for PIDE (partial integro-differential equation).

FIRST PASSAGE TIME UNDER A REGIME-SWITCHING JUMP-DIFFUSION MODEL AND ITS APPLICATION IN THE VALUATION OF PARTICIPATING CONTRACTS

  • Dong, Yinghui;Lv, Wenxin;Wu, Sang
    • Bulletin of the Korean Mathematical Society
    • /
    • v.56 no.5
    • /
    • pp.1355-1376
    • /
    • 2019
  • We investigate the valuation of participating life insurance policies with default risk under a geometric regime-switching jump-diffusion process. We derive explicit formula for the Laplace transform of the price of participating contracts by solving integro-differential system and then price them by inverting Laplace transforms.

A FAST AND ROBUST NUMERICAL METHOD FOR OPTION PRICES AND GREEKS IN A JUMP-DIFFUSION MODEL

  • JEONG, DARAE;KIM, YOUNG ROCK;LEE, SEUNGGYU;CHOI, YONGHO;LEE, WOONG-KI;SHIN, JAE-MAN;AN, HYO-RIM;HWANG, HYEONGSEOK;KIM, HJUNSEOK
    • The Pure and Applied Mathematics
    • /
    • v.22 no.2
    • /
    • pp.159-168
    • /
    • 2015
  • Abstract. We propose a fast and robust finite difference method for Merton's jump diffusion model, which is a partial integro-differential equation. To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. Also, we use non-uniform grids to increase efficiency. We present numerical experiments such as evaluation of the option prices and Greeks to demonstrate a performance of the proposed numerical method. The computational results are in good agreements with the exact solutions of the jump-diffusion model.

Characterization of Internal Reorientation of Methyl Group in 2,6-Dichlorotoluene

  • Nam-Goong, Hyun;Rho, Jung-Rae
    • Journal of the Korean Magnetic Resonance Society
    • /
    • v.13 no.1
    • /
    • pp.35-55
    • /
    • 2009
  • The two correlation times previously obtained in our coupled $^{13}C$ relaxation measurement for the methyl group in 2,6-dichlorotoluene may be used as a criterion for evaluating the reorientation dynamics of an internal rotor. We numerically tested an extended diffusion model and the Smoluchowski diffusion equation to see how the rotational inertial effect and jump character contribute to the internal correlation time ratio of the internal rotor. We also analytically solved the general jump model with three different rate constants in a sixfold symmetric potential barrier. By assuming that the internal rotation of the methyl group in 2,6-dichlorotoluene can be described in terms of jumps among sixfold harmonic potential wells, we can conclude that the jump model satisfactorily reproduce the experimental data and the rate for sixfold jump is at least 1.53 times as great as that of a threefold jump.