scholarly journals Pricing of Proactive Hedging European Option with Dynamic Discrete Position Strategy

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Meng Li ◽  
Xuefeng Wang ◽  
Fangfang Sun
Keyword(s):  
Brownian Motion ◽  
Lower Cost ◽  
Asset Price ◽  
Trading Strategy ◽  
Options Market ◽  
European Option ◽  
Practical Application ◽  
Underlying Asset ◽  
Exotic Option ◽  
Geometric Fractional Brownian Motion

Proactive hedging European option is an exotic option for hedgers in the options market proposed recently by Wang et al. It extends the classical European option by requiring option holders to continuously trade in underlying assets according to a predesigned trading strategy, to proactively hedge part of the potential risk from underlying asset price changes. To generalize this option design for practical application, in this study, a proactive hedging option with discrete trading strategy is developed and its pricing formula is deducted assuming the underlying asset price follows Geometric Fractional Brownian Motion. Simulation studies show that proactive hedging option with discrete trading strategy still enjoys strong price advantage compared to the classical European option for majority of parameter space. The observed price advantage is stronger when the underlying asset has more volatility or when the asset price follows closer to Geometric Brownian Motion. Additionally, we found that a higher frequency trading strategy has stronger price advantage if there is no trading cost. The findings in this research strongly facilitate the practical application of the proactive hedging option, making this lower-cost trading tool more feasible.

scholarly journals Proactive Hedging European Call Option Pricing with Linear Position Strategy

2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Meng Li ◽  
Xuefeng Wang ◽  
Fangfang Sun
Keyword(s):  
Asset Price ◽  
Stock Option ◽  
Call Option ◽  
European Option ◽  
Price Movement ◽  
Underlying Asset ◽  
European Call Option ◽  
Exotic Option ◽  
Risk Of Exposure ◽  
Geometric Fractional Brownian Motion

Proactive hedging option is an exotic European stock option designed for hedgers. Such option requires option holders to buy in (or sell out) the underlying asset (stock) and allows them to adjust the holdings of the underlying asset per its price changes within an option period. The proactive hedging option is an attractive choice for hedgers because its price is lower than that of classical options and because it completely hedges the risk of exposure for option holders. In this study, the underlying asset price movement is assumed to follow geometric fractional Brownian motion. The pricing formula for proactive hedging call options is derived with a linear position strategy by applying the risk-neutral evaluation principle. We use simulations to confirm that the price of this exotic option is always no more than that of the classical European option under the same parameters.

scholarly journals Series representation of the pricing formula for the European option driven by space-time fractional diffusion

2018 ◽  
Vol 21 (4) ◽  
pp. 981-1004 ◽  
Author(s):  
Jean-Philippe Aguilar ◽  
Cyril Coste ◽  
Jan Korbel
Keyword(s):  
Asset Price ◽  
Series Representation ◽  
Option Price ◽  
Double Series ◽  
Fractional Diffusion ◽  
Space Time ◽  
Esscher Transform ◽  
European Option ◽  
Underlying Asset ◽  
European Call Option

Abstract In this paper, we show that the price of an European call option, whose underlying asset price is driven by the space-time fractional diffusion, can be expressed in terms of rapidly convergent double-series. This series formula is obtained from the Mellin-Barnes representation of the option price with help of residue summation in ℂ2. We also derive the series representation for the associated risk-neutral factors, obtained by Esscher transform of the space-time fractional Green functions.

scholarly journals The Optimal Limit Prices of Limit Orders under an Extended Geometric Brownian Motion with Bankruptcy Risk

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 54
Author(s):  
Yu-Sheng Hsu ◽  
Pei-Chun Chen ◽  
Cheng-Hsun Wu
Keyword(s):  
Brownian Motion ◽  
Financial Markets ◽  
Asset Price ◽  
Trading Strategy ◽  
Geometric Brownian Motion ◽  
Price Model ◽  
Bankruptcy Risk ◽  
Limit Orders ◽  
Limit Price ◽  
Profit Functions

In the Black and Scholes system, the underlying asset price model follows geometric Brownian motion (GBM) with no bankruptcy risk. While GBM is a commonly used model in financial markets, bankruptcy risk should be considered in the case of a severe economic crisis, such as that caused by the COVID-19 pandemic. The omission of bankruptcy risk could considerably influence the setting of a trading strategy. In this article, we adopt an extended GBM model that considers the bankruptcy risk and study its optimal limit price problem. A limit order is a classical trading strategy for investing in stocks. First, we construct the explicit expressions of the expected discounted profit functions for sell and buy limit orders and then derive their optimal limit prices. Furthermore, via sensitivity analysis, we discuss the influence of the omission of bankruptcy risk in executing limit orders.

scholarly journals Pricing Vulnerable European Options under Lévy Process with Stochastic Volatility

2018 ◽  
Vol 2018 ◽  
pp. 1-16 ◽  
Author(s):  
Chaoqun Ma ◽  
Shengjie Yue ◽  
Yishuai Ren
Keyword(s):  
Stochastic Volatility ◽  
Asset Price ◽  
Option Price ◽  
Closed Form Solution ◽  
European Option ◽  
Short Term ◽  
Underlying Asset ◽  
Asset Value ◽  
Mean Reverting Process

This paper considers the pricing issue of vulnerable European option when the dynamics of the underlying asset value and counterparty’s asset value follow two correlated exponential Lévy processes with stochastic volatility, and the stochastic volatility is divided into the long-term and short-term volatility. A mean-reverting process is introduced to describe the common long-term volatility risk in underlying asset price and counterparty’s asset value. The short-term fluctuation of stochastic volatility is governed by a mean-reverting process. Based on the proposed model, the joint moment generating function of underlying log-asset price and counterparty’s log-asset value is explicitly derived. We derive a closed-form solution for the vulnerable European option price by using the Fourier inversion formula for distribution functions. Finally, numerical simulations are provided to illustrate the effects of stochastic volatility, jump risk, and counterparty credit risk on the vulnerable option price.

scholarly journals Pricing Collar Options with Stochastic Volatility

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Pengshi Li ◽  
Jianhui Yang
Keyword(s):  
Brownian Motion ◽  
Numerical Experiment ◽  
Stochastic Volatility ◽  
Asset Price ◽  
Analytical Approximation ◽  
Stochastic Volatility Model ◽  
Approximation Formula ◽  
Underlying Asset ◽  
Volatility Model ◽  
Mean Reverting Process

This paper studies collar options in a stochastic volatility economy. The underlying asset price is assumed to follow a continuous geometric Brownian motion with stochastic volatility driven by a mean-reverting process. The method of asymptotic analysis is employed to solve the PDE in the stochastic volatility model. An analytical approximation formula for the price of the collar option is derived. A numerical experiment is presented to demonstrate the results.

scholarly journals HOLDER-EXTENDIBLE EUROPEAN OPTION: CORRECTIONS AND EXTENSIONS

2015 ◽  
Vol 56 (4) ◽  
pp. 359-372 ◽  
Author(s):  
PAVEL V. SHEVCHENKO
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Real Life ◽  
Option Price ◽  
Geometric Brownian Motion ◽  
Fixed Amount ◽  
Underlying Asset ◽  
Closed Form Solutions ◽  
Pricing Options ◽  
Interest Rate Volatility

Financial contracts with options that allow the holder to extend the contract maturity by paying an additional fixed amount have found many applications in finance. Closed-form solutions for the price of these options have appeared in the literature for the case when the contract for the underlying asset follows a geometric Brownian motion with constant interest rate, volatility and nonnegative dividend yield. In this paper, option price is derived for the case of the underlying asset that follows a geometric Brownian motion with time-dependent drift and volatility, which is more important for real life applications. The option price formulae are derived for the case of a drift that includes nonnegative or negative dividend. The latter yields a solution type that is new to the literature. A negative dividend corresponds to a negative foreign interest rate for foreign exchange options, or storage costs for commodity options. It may also appear in pricing options with transaction costs or real options, where the drift is larger than the interest rate.

scholarly journals Tranching, CDS, and Asset Prices: How Financial Innovation Can Cause Bubbles and Crashes

2012 ◽  
Vol 4 (1) ◽  
pp. 190-225 ◽  
Author(s):  
Ana Fostel ◽  
John Geanakoplos
Keyword(s):  
Asset Prices ◽  
Asset Price ◽  
Financial Innovation ◽  
Underlying Asset

We show how the timing of financial innovation might have contributed to the mortgage bubble and then to the crash of 2007–2009. We show why tranching and leverage first raised asset prices and why CDS lowered them afterward. This may seem puzzling, since it implies that creating a derivative tranche in the securitization whose payoffs are identical to the CDS will raise the underlying asset price, while the CDS outside the securitization lowers it. The resolution of the puzzle is that the CDS lowers the value of the underlying asset since it is equivalent to tranching cash. (JEL E32, E44, G01, G12, G13, G21).

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