scholarly journals Turbo Warrants under Hybrid Stochastic and Local Volatility

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Min-Ku Lee ◽  
Ji-Hun Yoon ◽  
Jeong-Hoon Kim ◽  
Sun-Hwa Cho
Keyword(s):  
Stochastic Volatility ◽  
Uhlenbeck Process ◽  
Variance Model ◽  
Constant Elasticity ◽  
Local Volatility ◽  
Constant Elasticity Of Variance ◽  
Local Volatility Model ◽  
Volatility Model ◽  
Ornstein Uhlenbeck Process ◽  
Sensitive Structure

This paper considers the pricing of turbo warrants under a hybrid stochastic and local volatility model. The model consists of the constant elasticity of variance model incorporated by a fast fluctuating Ornstein-Uhlenbeck process for stochastic volatility. The sensitive structure of the turbo warrant price is revealed by asymptotic analysis and numerical computation based on the observation that the elasticity of variance controls leverage effects and plays an important role in characterizing various phases of volatile markets.

scholarly journals Pricing Arithmetic Asian Options under Hybrid Stochastic and Local Volatility

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Min-Ku Lee ◽  
Jeong-Hoon Kim ◽  
Kyu-Hwan Jang
Keyword(s):  
Stochastic Volatility ◽  
Option Price ◽  
Stochastic Volatility Model ◽  
Asian Options ◽  
Partial Differential ◽  
Constant Elasticity ◽  
Local Volatility ◽  
Constant Elasticity Of Variance ◽  
Arithmetic Average ◽  
Volatility Model

Recently, hybrid stochastic and local volatility models have become an industry standard for the pricing of derivatives and other problems in finance. In this study, we use a multiscale stochastic volatility model incorporated by the constant elasticity of variance to understand the price structure of continuous arithmetic average Asian options. The multiscale partial differential equation for the option price is approximated by a couple of single scale partial differential equations. In terms of the elasticity parameter governing the leverage effect, a correction to the stochastic volatility model is made for more efficient pricing and hedging of Asian options.

scholarly journals THE HESTON STOCHASTIC-LOCAL VOLATILITY MODEL: EFFICIENT MONTE CARLO SIMULATION

2014 ◽  
Vol 17 (07) ◽  
pp. 1450045 ◽  
Author(s):  
ANTHONIE W. VAN DER STOEP ◽  
LECH A. GRZELAK ◽  
CORNELIS W. OOSTERLEE
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Error Analysis ◽  
Stochastic Volatility ◽  
Numerical Experiments ◽  
Stochastic Volatility Model ◽  
Heston Model ◽  
Local Volatility ◽  
Local Volatility Model ◽  
Volatility Model

In this paper we propose an efficient Monte Carlo scheme for simulating the stochastic volatility model of Heston (1993) enhanced by a nonparametric local volatility component. This hybrid model combines the main advantages of the Heston model and the local volatility model introduced by Dupire (1994) and Derman & Kani (1998). In particular, the additional local volatility component acts as a "compensator" that bridges the mismatch between the nonperfectly calibrated Heston model and the market quotes for European-type options. By means of numerical experiments we show that our scheme enables a consistent and fast pricing of products that are sensitive to the forward volatility skew. Detailed error analysis is also provided.

Perpetual American put options in a level-dependent volatility model

2003 ◽  
Vol 40 (03) ◽  
pp. 783-789 ◽  
Author(s):  
Erik Ekström
Keyword(s):  
Stock Price ◽  
Variance Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Put Options ◽  
American Put Options ◽  
Volatility Model ◽  
American Put

We find the explicit value of perpetual American put options in the constant elasticity of variance model using the concept of smooth fit. We show that the price is increasing in the volatility and convex in the underlying stock price. Moreover, as the model converges to the standard Black and Scholes model, the value of the put is shown to approach the ‘correct’ limit.

Perpetual American put options in a level-dependent volatility model

2003 ◽  
Vol 40 (3) ◽  
pp. 783-789 ◽  
Author(s):  
Erik Ekström
Keyword(s):  
Stock Price ◽  
Variance Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Put Options ◽  
American Put Options ◽  
Volatility Model ◽  
American Put

We find the explicit value of perpetual American put options in the constant elasticity of variance model using the concept of smooth fit. We show that the price is increasing in the volatility and convex in the underlying stock price. Moreover, as the model converges to the standard Black and Scholes model, the value of the put is shown to approach the ‘correct’ limit.

scholarly journals A CORRELATED STOCHASTIC VOLATILITY MODEL MEASURING LEVERAGE AND OTHER STYLIZED FACTS

2002 ◽  
Vol 05 (05) ◽  
pp. 541-562 ◽  
Author(s):  
JAUME MASOLIVER ◽  
JOSEP PERELLÓ
Keyword(s):  
Stochastic Volatility ◽  
Heavy Tails ◽  
Stochastic Volatility Model ◽  
Market Model ◽  
Leverage Effect ◽  
Stylized Facts ◽  
Uhlenbeck Process ◽  
Volatility Model ◽  
Ornstein Uhlenbeck Process ◽  
Negative Skewness

We analyze a stochastic volatility market model in which volatility is correlated with return and is represented by an Ornstein-Uhlenbeck process. In the framework of this model we exactly calculate the leverage effect and other stylized facts, such as mean reversion, leptokurtosis and negative skewness. We also obtain a close analytical expression for the characteristic function and study the heavy tails of the probability distribution.

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