Systematic jump risks in a small open economy: simultaneous equilibrium valuation of options on the market portfolio and the exchange rate

Cao, Melanie

doi:10.1016/s0261-5606(00)00053-x

Cited by 8 publications

(11 citation statements)

References 31 publications

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“…We adopt the framework of a small open economy in Cao (2001) with a monetary component and take the bitcoin as the foreign currency. This small open economy consists of a single risk‐averse representative agent with an infinite lifetime horizon.…”

Section: A Small Open Monetary Economymentioning

confidence: 99%

“…This small open economy consists of a single risk‐averse representative agent with an infinite lifetime horizon. In Cao (2001), the representative agent has a log utility which prevents us from studying the impact of risk‐aversion on asset prices. To remedy this while maintaining analytical tractability, we extend the log utility preference in Cao (2001) to the following:

U (c_{t}, m_{t}, t)) = e^{- ρ t} ([], α \frac{c_{t}^{γ + 1}}{γ + 1} + (1 - α)) \ln m_{t}),

where

γ

measures the risk‐aversion attitude of the representative agent.…”

Section: A Small Open Monetary Economymentioning

confidence: 99%

“…The framework in Cao (2001) offers all of the above features and is therefore adopted by treating bitcoin as the foreign currency and by generalizing the log‐utility to a power utility so as to study the effect of risk‐aversion. In the small open economy, money has a nontrivial role in the representative agent's utility function.…”

Section: Introductionmentioning

confidence: 99%

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Valuation of bitcoin options

Celik

2021

Journal of Futures Markets

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We propose an equilibrium valuation model for bitcoin options by extending Cao. Bitcoin is interpreted as a foreign currency in a small open economy where money supply and aggregate dividend are exogenous. The equilibrium bitcoin prices increase with diffusive and jump risks of these two exogenous factors. Analytical option pricing formulas are obtained with Merton's model as a special case. Static analysis reveals that a bitcoin call (put) option value increases (decreases) with the money supply growth rate. Numerical analysis shows that all risks lead to a positive premium in option prices relative to the Black–Scholes model.

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Section: A Small Open Monetary Economymentioning

confidence: 99%

U (c_{t}, m_{t}, t)) = e^{- ρ t} ([], α \frac{c_{t}^{γ + 1}}{γ + 1} + (1 - α)) \ln m_{t}),

where

γ

measures the risk‐aversion attitude of the representative agent.…”

Section: A Small Open Monetary Economymentioning

confidence: 99%

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Valuation of bitcoin options

Celik

2021

Journal of Futures Markets

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“…However, they did not consider the valuation of currency options. Cao (2001) proposed the small open economy. She obtained a closed form formula of the currency option and stock options under a jump-diffusion model.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium valuation of currency options under a jump-diffusion model with stochastic volatility

Xing

Yang

2015

Journal of Computational and Applied Mathematics

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Please cite this article as: Y. Xing, X. Yang, Equilibrium valuation of currency options under a jump-diffusion model with stochastic volatility, Journal of Computational and Applied Mathematics (2014), http://dx. AbstractIn this paper, we continue to investigate the model related to Bakshi and Chen (1997). In our model, both of the money supplies in the two countries are assumed to follow jump-diffusion processes with stochastic volatility. In the set of the two-country economy, we obtain the equilibrium price of the nominal exchange rate. With the help of Fourier transform to solve a partial integro-differential equation (PIDE), we get a closedform solution to the PIDE for a European call currency option. We also do Monte Carlo simulations to verify the correctness of the derived formula. Our model contains some existing currency option models as special cases, for example the stochastic-volatility jumpdiffusion (SVJD) model in Bates(1996), in which the jump of the exchange rate is driven by one Poisson process. We also provide some numerical analysis to show that our model is effective to the foreign currency option market.

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“…4 Cao (2001) employs a general equilibrium analysis to value options on the market portfolio and the exchange rate. We provide the comparative statistics and numerical analysis that are not examined by Cao (2001). jump risks may well be nonsystematic if those risks are firm-specific.…”

Section: Introductionmentioning

confidence: 99%

The pricing of foreign currency options under jump‐diffusion processes

Ahn

Cho

Park

2007

Journal of Futures Markets

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In this article, the authors derive explicit formulas for European foreign exchange (FX) call and put option values when the exchange rate dynamics are governed by jump-diffusion processes. The authors use a simple general equilibrium international asset pricing model with continuous trading and frictionless international capital markets. The domestic and foreign price level are introduced as state variables that contain jumps caused by monetary shocks and catastrophic events such as 9/11 or Hurricane Katrina. The domestic and foreign interest rates are stochastic and endogenously determined in the model and are shown to be critically affected by the jump risk of the foreign exchange. The model shows thatWe would like to thank a referee and the editor for their valuable comments.1 Cox and Ross (1976) and Jones (1984) have derived option pricing formula by assuming deterministic jump amplitudes. 2 A stock option formula under jump-diffusion processes has been derived by Merton (1976). the behavior of FX options is affected through the impact of state variables and parameters on the nominal interest rates. The model contrasts with those of M. Garman and S. Kohlhagen (1983) andO. Grabbe (1983), whose models have exogenously determined interest rates.

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Systematic jump risks in a small open economy: simultaneous equilibrium valuation of options on the market portfolio and the exchange rate

Cited by 8 publications

References 31 publications

Valuation of bitcoin options

Valuation of bitcoin options

Equilibrium valuation of currency options under a jump-diffusion model with stochastic volatility

The pricing of foreign currency options under jump‐diffusion processes

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