On the exercise of American quanto options

Battauz, Anna; Donno, Marzia De; Sbuelz, Alessandro

doi:10.1016/j.najef.2022.101738

Cited by 8 publications

(3 citation statements)

References 36 publications

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“…Our finding supplements [20,24] who extend to the Lévy market the findings by [10]. An analogous result for the negative discount rate case was obtained in [4][5][6]17]. A comprehensive review of the put-call duality for American options is given in [18].…”

Section: Introductionsupporting

confidence: 82%

Perpetual American Options with Asset-Dependent Discounting

Al-Hadad,

Palmowski

2023

Appl Math Optim

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In this paper we consider the following optimal stopping problem $$\begin{aligned} V^{\omega }_{\text {A}}(s) = \sup _{\tau \in {\mathcal {T}}} {\mathbb {E}}_{s}[e^{-\int _0^\tau \omega (S_w) dw} g(S_\tau )], \end{aligned}$$ V A ω ( s ) = sup τ ∈ T E s [ e - ∫ 0 τ ω ( S w ) d w g ( S τ ) ] , where the process $$S_t$$ S t is a jump-diffusion process, $${\mathcal {T}}$$ T is a family of stopping times while g and $$\omega $$ ω are fixed payoff function and discount function, respectively. In a financial market context, if $$g(s)=(K-s)^+$$ g ( s ) = ( K - s ) + or $$g(s)=(s-K)^+$$ g ( s ) = ( s - K ) + and $${\mathbb {E}}$$ E is the expectation taken with respect to a martingale measure, $$V^{\omega }_{\text {A}}(s)$$ V A ω ( s ) describes the price of a perpetual American option with a discount rate depending on the value of the asset process $$S_t$$ S t . If $$\omega $$ ω is a constant, the above problem produces the standard case of pricing perpetual American options. In the first part of this paper we find sufficient conditions for the convexity of the value function $$V^{\omega }_{\text {A}}(s)$$ V A ω ( s ) . This allows us to determine the stopping region as a certain interval and hence we are able to identify the form of $$V^{\omega }_{\text {A}}(s)$$ V A ω ( s ) . We also present a put-call symmetry for American options with asset-dependent discounting. In the case when $$S_t$$ S t is a spectrally negative geometric Lévy process we give exact expressions using the so-called omega scale functions introduced in [30]. We show that the analysed value function satisfies the HJB equation and we give sufficient conditions for the smooth fit property as well. Finally, we present a few examples for which we obtain the analytical form of the value function $${V}^{\omega }_{\text {A}}(s)$$ V A ω ( s ) .

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Section: Introductionsupporting

confidence: 82%

Perpetual American Options with Asset-Dependent Discounting

Al-Hadad,

Palmowski

2023

Appl Math Optim

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“…Moreover, Teng et al [ 6 ] assumed that the correlation between the underlying asset and currency exchange rate is dynamic, and they found that this dynamic correlation had a significant impact on the quanto option pricing. Battauz et al [ 7 ] studied the optimal exercise policies of American quanto options by using a parsimonious diffusive model, which further enriched the pricing theory of quanto options. Recently, Lee et al [ 8 ] studied partial quanto lookback options and proposed an approach to evaluating the option.…”

Section: Introductionmentioning

confidence: 99%

Pricing quanto options with market liquidity risk

Gao,

Bai

2023

PLoS ONE

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This paper investigates the pricing problem of quanto options with market liquidity risk using the Bayesian method. The increasing volatility of global financial markets has made liquidity risk a significant factor that should be taken into consideration while evaluating option prices. To address this issue, we first derive the pricing formula for quanto options with liquidity risk. Next, we construct a likelihood function to conduct posterior inference on model parameters. We then propose a numerical algorithm to conduct statistical inferences on the option prices based on the posterior distribution. This proposed method considers the impact of parameter uncertainty on option prices. Finally, we conduct a comparison between the Bayesian method and traditional estimation methods to examine their validity. Empirical results show that our proposed method is feasible for pricing and predicting quanto options with liquidity risk, particularly for parameter estimations with a small sample size.

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“…In order to better capture market characteristics, such as volatility smile, heavy tails, skewness and jump, the existing literatures incorporate these features into quanto option model, for example GARCH models, stochastic volatility models and jump-diffusion models, etc. More related research refers to [2,3,4,5,6].…”

Section: Introductionmentioning

confidence: 99%

Posterior inference on Quanto option pricing model with liquidity-adjustment

Gao

Bai

2022

Preprint

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This paper proposes an alternative approach to estimate parameters and evaluate the quanto option with stock liquidity under Bayesian framework. First, we derive an explicit expression of the quanto option price with liquidity-adjustment in an alternative way. Then, an applicable likelihood is proposed to conduct posterior inference on model parameters based on the joint distribution of underlying stock price dynamics and the exchange rate process, which provides a new perspective to estimate the correlation coefficient. Moreover, the statistical inference on the quanto option price is conducted by the posterior distribution and numerical algorithm. The proposed method considers the impact of parameter uncertainty on option prices, particularly the correlation coefficient randomness. Finally, the numerical analysis is performed for examining the effectiveness of the proposed method in terms of estimating parameters and pricing quanto options. Empirical results indicate that the proposed method is feasible in pricing and predicting quanto option with liquidity-adjustment.

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On the exercise of American quanto options

Cited by 8 publications

References 36 publications

Perpetual American Options with Asset-Dependent Discounting

Perpetual American Options with Asset-Dependent Discounting

Pricing quanto options with market liquidity risk

Posterior inference on Quanto option pricing model with liquidity-adjustment

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