# American Institute of Mathematical Sciences

• Previous Article
Analysis of dynamic service system between regular and retrial queues with impatient customers
• JIMO Home
• This Issue
• Next Article
Bargaining in a multi-echelon supply chain with power structure: KS solution vs. Nash solution
doi: 10.3934/jimo.2020060

## Effect of institutional deleveraging on option valuation problems

 1 Advanced Modeling and Applied Computing Laboratory, Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong 2 School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, China

* Corresponding author: Na Song

Received  March 2019 Revised  November 2019 Published  March 2020

This paper studies the valuation problem of European call options when the presence of distressed selling may lead to further endogenous volatility and correlation between the stock issuer's asset value and the price of the stock underlying the option, and hence influence the option price. A change of numéraire technique, based on Girsanov Theorem, is applied to derive the analytical pricing formula for the European call option when the price of underlying stock is subject to price pressure triggered by the stock issuer's own distressed selling. Numerical experiments are also provided to study the impacts of distressed selling on the European call option prices.

Citation: Qing-Qing Yang, Wai-Ki Ching, Wan-Hua He, Na Song. Effect of institutional deleveraging on option valuation problems. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020060
##### References:

show all references

##### References:
Variation of European Call Option with Respect to Distressed Selling Impact
Variation of Delta of a European Call Option with Respect to Distressed Selling Impact
Variation of Vega of a European Call Option with Respect to Distressed Selling Impact
Variation of Gamma of a European Call Option with Respect Distressed Selling Impact
Variation of European Call Option Price with Respect to Distressed Selling Impact. $f = \frac{\log{x}}{\eta}$
Variation of European Call Option Price with Respect to Distressed Selling Impact. $f = \frac{1-e^x}{\eta}$
Greeks
 Option Price($C(t)$) $S(t)\mathcal{N}(d_+(t))-KB(t,T)\mathcal N(d_-(t))$ Delta($\Delta$) $\mathcal N(d_+(t))$ Vega($\mathcal V$) $S(t) n(d_+(t))\sqrt{T-t}$ Gamma($\Gamma$) $\frac{ n(d_+)}{S(t)\bar{\sigma}_t\sqrt{T-t}}$
 Option Price($C(t)$) $S(t)\mathcal{N}(d_+(t))-KB(t,T)\mathcal N(d_-(t))$ Delta($\Delta$) $\mathcal N(d_+(t))$ Vega($\mathcal V$) $S(t) n(d_+(t))\sqrt{T-t}$ Gamma($\Gamma$) $\frac{ n(d_+)}{S(t)\bar{\sigma}_t\sqrt{T-t}}$
Preference parameters
 Parameters Values Parameters Values Market depth $L=10$ MLR $\eta=1$ Volatility $\sigma_S=0.2$ Volatility $\sigma_X=0.1$ Volatility $\sigma_r=0.15$ Time to maturity $T-t=1$ Initial price $S_0=40$ Strike price $K=40$ Initial price $X_0=100$ Initial price $B(t,T)=0.05$ Correlation $\rho=0.7$ Time steps $N=100$ Correlation $\rho_{1r}=0.5$ Correlation $\rho_{2r}=0.6$ Mean-reverting speed $a=100$ Long-term interest rate $b=0.0243$
 Parameters Values Parameters Values Market depth $L=10$ MLR $\eta=1$ Volatility $\sigma_S=0.2$ Volatility $\sigma_X=0.1$ Volatility $\sigma_r=0.15$ Time to maturity $T-t=1$ Initial price $S_0=40$ Strike price $K=40$ Initial price $X_0=100$ Initial price $B(t,T)=0.05$ Correlation $\rho=0.7$ Time steps $N=100$ Correlation $\rho_{1r}=0.5$ Correlation $\rho_{2r}=0.6$ Mean-reverting speed $a=100$ Long-term interest rate $b=0.0243$
 [1] Ripeng Huang, Shaojian Qu, Xiaoguang Yang, Zhimin Liu. Multi-stage distributionally robust optimization with risk aversion. Journal of Industrial & Management Optimization, 2021, 17 (1) : 233-259. doi: 10.3934/jimo.2019109 [2] Haodong Yu, Jie Sun. Robust stochastic optimization with convex risk measures: A discretized subgradient scheme. Journal of Industrial & Management Optimization, 2021, 17 (1) : 81-99. doi: 10.3934/jimo.2019100 [3] Hongguang Ma, Xiang Li. Multi-period hazardous waste collection planning with consideration of risk stability. Journal of Industrial & Management Optimization, 2021, 17 (1) : 393-408. doi: 10.3934/jimo.2019117 [4] Editorial Office. Retraction: Xiao-Qian Jiang and Lun-Chuan Zhang, A pricing option approach based on backward stochastic differential equation theory. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 969-969. doi: 10.3934/dcdss.2019065 [5] Haixiang Yao, Ping Chen, Miao Zhang, Xun Li. Dynamic discrete-time portfolio selection for defined contribution pension funds with inflation risk. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020166 [6] Youming Guo, Tingting Li. Optimal control strategies for an online game addiction model with low and high risk exposure. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020347 [7] Wenyuan Wang, Ran Xu. General drawdown based dividend control with fixed transaction costs for spectrally negative Lévy risk processes. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020179 [8] Chang-Yuan Cheng, Shyan-Shiou Chen, Rui-Hua Chen. Delay-induced spiking dynamics in integrate-and-fire neurons. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020363 [9] Hai Huang, Xianlong Fu. Optimal control problems for a neutral integro-differential system with infinite delay. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020107 [10] Eric Foxall. Boundary dynamics of the replicator equations for neutral models of cyclic dominance. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1061-1082. doi: 10.3934/dcdsb.2020153 [11] Puneet Pasricha, Anubha Goel. Pricing power exchange options with hawkes jump diffusion processes. Journal of Industrial & Management Optimization, 2021, 17 (1) : 133-149. doi: 10.3934/jimo.2019103 [12] Musen Xue, Guowei Zhu. Partial myopia vs. forward-looking behaviors in a dynamic pricing and replenishment model for perishable items. Journal of Industrial & Management Optimization, 2021, 17 (2) : 633-648. doi: 10.3934/jimo.2019126

2019 Impact Factor: 1.366

## Tools

Article outline

Figures and Tables