Efficient Pricing of Derivatives on Assets with Discrete Dividends

Vellekoop, Michel; Nieuwenhuis, J.W.

doi:10.1080/13504860600563077

Cited by 66 publications

(48 citation statements)

References 13 publications

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“…Figure 1 plots the exercise boundary t → c 1 (t) of the Put option with strike K = 100 and maturity T = 4 in the model (0.1) with r = 0.04, σ = 0.3, t 1 d = 3.5 and proportional dividends with ρ 1 = 0.05. This exercise boundary was computed by a binomial tree method (see [22]). …”

Section: Lemma 13mentioning

confidence: 99%

Regularity of the Exercise Boundary for American Put Options on Assets with Discrete Dividends

Jourdain¹,

Vellekoop²

2011

SIAM J. Finan. Math.

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We analyze the regularity of the optimal exercise boundary for the American Put option when the underlying asset pays a discrete dividend at a known time t d during the lifetime of the option. The ex-dividend asset price process is assumed to follow Black-Scholes dynamics and the dividend amount is a deterministic function of the ex-dividend asset price just before the dividend date. The solution to the associated optimal stopping problem can be characterised in terms of an optimal exercise boundary which, in contrast to the case when there are no dividends, may no longer be monotone. In this paper we prove that when the dividend function is positive and concave, then the boundary is non-increasing in a left-hand neighbourhood of t d , and tends to 0 as time tends to t − d with a speed that we can characterize. When the dividend function is linear in a neighbourhood of zero, then we show continuity of the exercise boundary and a high contact principle in the left-hand neighbourhood of t d . When it is globally linear, then right-continuity of the boundary and the high contact principle are proved to hold globally. Finally, we show how all the previous results can be extended to multiple dividend payment dates in that case.

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Section: Lemma 13mentioning

confidence: 99%

Regularity of the Exercise Boundary for American Put Options on Assets with Discrete Dividends

Jourdain¹,

Vellekoop²

2011

SIAM J. Finan. Math.

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“…On Figure 2, we represent two different exercise boundaries computed through a binomial tree method following [VN06]. In both cases, c 1 (0) = κ 1 = 20.…”

Section: Left Continuitymentioning

confidence: 99%

“…In case (a), the boundary appears to be smooth whereas in case (b), it seems to be merely continuous (at time 0.04, even continuity is not so clear from the figure). Figure 3 are represented two different exercise boundaries computed through a binomial tree method following [VN06]. Notice that in each case, a dividend is paid if the stock price is over 50.…”

Section: Left Continuitymentioning

confidence: 99%

Regularity of the American Put option in the Black–Scholes model with general discrete dividends

Jeunesse

Jourdain

2012

Stochastic Processes and their Applications

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We analyze the regularity of the value function and of the optimal exercise boundary of the American Put option when the underlying asset pays a discrete dividend at known times during the lifetime of the option. The ex-dividend asset price process is assumed to follow the Black-Scholes dynamics and the dividend amount is a deterministic function of the ex-dividend asset price just before the dividend date. This function is assumed to be non-negative, non-decreasing and with growth rate not greater than 1. We prove that the exercise boundary is continuous and that the smooth contact property holds for the value function at any time but the dividend dates. We thus extend and generalize the results obtained in [JV11] when the dividend function is also positive and concave. Lastly, we give conditions on the dividend function ensuring that the exercise boundary is locally monotonic in a neighborhood of the corresponding dividend date.

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“…The dividend payment was always equal to D i = 0.20, (i = 1, 2, 3). The adjustments made to cover the dividend dates were based on standard interpolation techniques, see Vellekoop and Nieuwenhuis (2006) for a detailed description. We left the other parameters as in (5.1), and we took √ V 0 = 50% and S 0 = K = 10.…”

Section: Optimal Exercise Surfacementioning

confidence: 99%