Pricing stock options with stochastic interest rate

Abudy, Menachem; Izhakian, Yehuda

doi:10.1504/ijpam.2013.054408

Cited by 21 publications

(8 citation statements)

References 30 publications

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“…The numerical examples for the European options under the Vasicek interest rate model are listed in Table 6. The true values are calculated using the analytic formula [9,19]. Our seven-term solution (Φ 7 ) gives option values with an AAE of the order of 10 −7 .…”

Section: Numerical Resultsmentioning

confidence: 99%

“…where σ B = σ B (t) is the volatility and is time-dependent. From equations (9) and (27) of Vasicek [30], σ B is given by σ B = σ 2 [1 − exp{−a(T − t)}]/a. Since the bond is a traded security, the drift rate of the bond price under the risk-neutral measure is simply given by the risk-free rate r. We suppose that the changes in W 1 and W 2 are correlated with coefficient ρ, that is, dW 1 dW 2 = ρdt.…”

Section: Pricing European Options Depend On a Vasicek Interest Ratementioning

confidence: 99%

“…For more details on the derivation, we refer the reader to the work of Fang [19]. At expiry, The put-call parity for the aforementioned European options is given by Abudy and Izhakian [9]. Therefore, it suffices to give details of the derivation for the put option alone.…”

Section: Pricing European Options Depend On a Vasicek Interest Ratementioning

confidence: 99%

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An Appropriate Approach to Pricing European-Style Options With the Adomian Decomposition Method

Goard

Zhu

2018

ANZIAM J.

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We study the numerical Adomian decomposition method for the pricing of European options under the well-known Black–Scholes model. However, because of the nondifferentiability of the pay-off function for such options, applying the Adomian decomposition method to the Black–Scholes model is not straightforward. Previous works on this assume that the pay-off function is differentiable or is approximated by a continuous estimation. Upon showing that these approximations lead to incorrect results, we provide a proper approach, in which the singular point is relocated to infinity through a coordinate transformation. Further, we show that our technique can be extended to pricing digital options and European options under the Vasicek interest rate model, in both of which the pay-off functions are singular. Numerical results show that our approach overcomes the difficulty of directly dealing with the singularity within the Adomian decomposition method and gives very accurate results.

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Section: Numerical Resultsmentioning

confidence: 99%

Section: Pricing European Options Depend On a Vasicek Interest Ratementioning

confidence: 99%

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An Appropriate Approach to Pricing European-Style Options With the Adomian Decomposition Method

Goard

Zhu

2018

ANZIAM J.

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“…The findings show that the SVLL model has the smallest RMSE for the single index calibration, i.e., the stochastic volatility and liquidity model with leverage effects is the best candidate for the stock price process. Capturing additional sources of uncertainty appears to have a considerable effect on option prices and demonstrate a significant pricing improvement (Abudy and Izhakian 2013). On average, I also have smaller sell side market depths.…”

Section: Calibration In Index Option Marketsmentioning

confidence: 94%

Option Implied Stock Buy-Side and Sell-Side Market Depths

Tsai¹

2019

Risks

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This paper investigates option valuation when the underlying market suffers from illiquidity of price impact. Using option data, I infer trading activities and price impacts on the buy side and the sell side in the stock market from option prices across maturities. The finding displays that the stock market is active when the stock prices plummet, but becomes silent after the market crashes. In addition, the difference of option implied price impacts between the buy side and the sell side, which indicates asymmetric liquidity, increases with the time to maturity, especially on the day of the market crisis. Moreover, investors have different perspectives on the future liquidity after liquidity shocks when they are in a bull market or in a bear market according to the option implied price impact (or market depth) curves. I also calibrate three market indices simultaneously and reach the same conclusion that the three markets become erratic on the event date and calm down in the aftermath.

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“…The Black-Scholes model has undergone a number of improvements that have incorporated stochastic volatility, the jump behaviour of asset returns and stochastic interest rates (Abudy and Izhakian 2013). We incorporate these improvements in the following section.…”

Section: Introductionmentioning

confidence: 99%

Pricing credit-risky bonds and spread options modelling credit-spread term structures with two-dimensional Markov-modulated jump-diffusion

Chen

Hsu

2015

Quantitative Finance

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The relationship between company hazard rates and the business cycle becomes more apparent after a financial crisis. To address this relationship, a regime-switching process with an intensity function is adopted in this paper. In addition, the dynamics of both interest rates and asset values are modelled with a Markov-modulated jump-diffusion model, and a 2-factor hazard rate model is also considered. Based on this more suitable model setting, a closed-form model of pricing risky bonds is derived. The difference in yield between a risky bond and risk-free zero coupon bond is used to model a term structure of credit spreads (CSs) from which a closed-form pricing model of a call option on CSs is obtained. In addition, the degree to which the explicit regime shift affects CSs and credit-risky bond prices is numerically examined using three forward-rate functions under various business-cycle patterns.

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Pricing stock options with stochastic interest rate

Cited by 21 publications

References 30 publications

An Appropriate Approach to Pricing European-Style Options With the Adomian Decomposition Method

An Appropriate Approach to Pricing European-Style Options With the Adomian Decomposition Method

Option Implied Stock Buy-Side and Sell-Side Market Depths

Pricing credit-risky bonds and spread options modelling credit-spread term structures with two-dimensional Markov-modulated jump-diffusion

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