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 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 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.

PRICING FORMULA FOR EXCHANGE OPTION BASED ON STOCHASTIC DELAY DIFFERENTIAL EQUATION WITH JUMPS

2020 ◽  
pp. 1-16
Author(s):  
Kyong-Hui Kim ◽  
Jong-Kuk Kim ◽  
Ho-Bom Jo
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Asset Price ◽  
Call Option ◽  
Stochastic Delay Differential Equations ◽  
Underlying Asset ◽  
Stochastic Delay ◽  
European Call Option ◽  
Delay Differential ◽  
Exchange Option

This paper deals with pricing formulae for a European call option and an exchange option in the case where underlying asset price processes are represented by stochastic delay differential equations with jumps (hereafter “SDDEJ”). We introduce a new model in which Poisson jumps are added in stochastic delay differential equations to capture behaviors of an underlying asset process more precisely. We derive explicit pricing formulae for the European call option and the exchange option by proving a Lemma on the conditional expectation. Finally, we show that our “SDDEJ” model is meaningful through some numerical experiments and discussions.

Alternative Formulas to Compute Implied Standard Deviation

2009 ◽  
Vol 12 (02) ◽  
pp. 159-176 ◽  
Author(s):  
James S. Ang ◽  
Gwoduan David Jou ◽  
Tsong-Yue Lai
Keyword(s):  
Standard Deviation ◽  
Closed Form ◽  
Asset Price ◽  
Closed Form Solution ◽  
Form Solution ◽  
Call Option ◽  
Present Value ◽  
Underlying Asset ◽  
The Third ◽  
Exercise Price

We assume that the call option's value is correctly priced by Black and Scholes' option pricing model in this paper. This paper derives an exact closed-form solution for implied standard deviation under the condition that the underlying asset price equals the present value of the exercise price. The exact closed-form solution provides the true implied standard deviation and has no estimate error. This paper also develops three alternative formulas to estimate the implied standard deviation if this condition is violated. Application of the Taylor expansion on a single call option value derives the first formula. The accuracy of this formula depends on the deviation between the underlying asset price and the present value of the exercise price. Use of the Taylor formula on two call option prices with different exercise prices is used to develop the second formula, which can be used even though the underlying asset price deviates significantly from the present value of the exercise price. Extension of the second formula's approach to third options value derives the third formula. A merit of the third formula is to circumvent a required parameter used in the second formula. Simulations demonstrate that the implied standard deviations calculated by the second and third formulas provide accurate estimates of the true implied standard deviations.

STOCHASTIC VOLATILITY

2002 ◽  
Vol 05 (05) ◽  
pp. 515-530 ◽  
Author(s):  
SOTIRIOS SABANIS
Keyword(s):  
Brownian Motion ◽  
Stochastic Volatility ◽  
Series Representation ◽  
Random Variable ◽  
Call Option ◽  
Underlying Asset ◽  
European Call Option ◽  
Practical Convergence ◽  
Security Price ◽  
Simulation Results

Hull and White [1] have priced a European call option for the case in which the volatility of the underlying asset is a lognormally distributed random variable. They have obtained their formula under the assumption of uncorrelated innovations in security price and volatility. Although the option pricing formula has a power series representation, the question of convergence has been left unanswered. This paper presents an iterative method for calculating all the higher order moments of volatility necessary for the process of proving convergence theoretically. Moreover, simulation results are given that show the practical convergence of the series. These results have been obtained by using a displaced geometric Brownian motion as a volatility process.

scholarly journals Estimasi Harga Multi-State European Call Option Menggunakan Model Binomial

CAUCHY ◽  
2011 ◽  
Vol 1 (4) ◽  
pp. 182
Author(s):  
Mila Kurniawaty, Endah Rokhmati ◽  
Endah Rokhmati
Keyword(s):  
Mean Square Error ◽  
Mean Square ◽  
Call Option ◽  
Expiration Date ◽  
Strike Price ◽  
Underlying Asset ◽  
Put Option ◽  
European Call Option ◽  
Black Scholes

Option merupakan kontrak yang memberikan hak kepada pemiliknya untuk membeli (call option) atau menjual (put option) sejumlah aset dasar tertentu (underlying asset) dengan harga tertentu (strike price) dalam jangka waktu tertentu (sebelum atau saat expiration date). Perkembangan option belakangan ini memunculkan banyak model pricing untuk mengestimasi harga option, salah satu model yang digunakan adalah formula Black-Scholes. Multi-state option merupakan sebuah option yang payoff-nya didasarkan pada dua atau lebih aset dasar. Ada beberapa metode yang dapat digunakan dalam mengestimasi harga call option, salah satunya masyarakat finance sering menggunakan model binomial untuk estimasi berbagai model option yang lebih luas seperti multi-state call option. Selanjutnya, dari hasil estimasi call option dengan model binomial didapatkan formula terbaik berdasarkan penghitungan eror dengan mean square error. Dari penghitungan eror didapatkan eror rata-rata dari masing-masing formula pada model binomial. Hasil eror rata-rata menunjukkan bahwa estimasi menggunakan formula 5 titik lebih baik dari pada estimasi menggunakan formula 4 titik.

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 Interval European Option with the Principle of Maximum Entropy

Entropy ◽  
2019 ◽  
Vol 21 (8) ◽  
pp. 788 ◽  
Author(s):  
Xiao Liu ◽  
Rongxi Zhou ◽  
Yahui Xiong ◽  
Yuexiang Yang
Keyword(s):  
Maximum Entropy ◽  
Stock Exchange ◽  
The United States ◽  
Stock Option ◽  
European Option ◽  
Entropy Model ◽  
Underlying Asset ◽  
European Option Pricing ◽  
Asset Distribution ◽  
Principle Of Maximum

This paper develops the interval maximum entropy model for the interval European option valuation by estimating an underlying asset distribution. The refined solution for the model is obtained by the Lagrange multiplier. The particle swarm optimization algorithm is applied to calculate the density function of the underlying asset, which can be utilized to price the Shanghai Stock Exchange (SSE) 50 Exchange Trades Funds (ETF) option of China and the Boeing stock option of the United States. Results show that maximum entropy distribution provides precise estimations for the underlying asset of interval number situations. In this way, we can get the distribution of the underlying assets and apply it to the interval European option pricing in the financial market.

A NOTE ON PERTURBATION ANALYSIS ESTIMATORS FOR AMERICAN-STYLE OPTIONS

2000 ◽  
Vol 14 (3) ◽  
pp. 385-392 ◽  
Author(s):  
Michael C. Fu* ◽  
Rongwen Wu ◽  
Gül Gürkan ◽  
A. Yonca Demir
Keyword(s):  
Perturbation Analysis ◽  
Asset Price ◽  
Previous Model ◽  
Call Option ◽  
Price Model ◽  
Underlying Asset ◽  
Asset Price Model ◽  
American Style

In this note, we correct an error in the paper by Fu and Hu [1] for the perturbation analysis estimator given for the gradient of an American call option payoff on an underlying asset paying multiple dividends. We then introduce a different asset price model that is more straightforward than the previous model, and derive the corresponding gradient estimators. We conclude with a brief discussion of extensions of the estimator to other American-style options.

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