Perpetual American options in incomplete markets: the infinitely divisible case

Henderson, Vicky; Hobson, David

doi:10.1080/14697680701400986

Cited by 6 publications

(7 citation statements)

References 17 publications

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“…Equation (4.6) can be solved by considering the inverse function H = h −1 , so that dH/dz = −(k 1 (1 + δ) + (1 − δ)z)/(γ z(z − k 1 ) 2 ). It is easily verified (see Henderson and Hobson 2008 for details) that in the case δ ≤ 1, h(0) = ∞ and…”

Section: A Portfolio Of Options With Different Strikesmentioning

confidence: 92%

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Optimal Liquidation of Derivative Portfolios

Henderson

Hobson

2011

Mathematical Finance

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We consider the problem facing a risk-averse agent who seeks to liquidate or exercise a portfolio of (infinitely divisible) perpetual American-style options on a single underlying asset. The optimal liquidation strategy is of threshold form and can be characterized explicitly as the solution of a calculus of variations problem. Apart from a possible initial exercise of a tranche of options, the optimal behavior involves liquidating the portfolio in infinitesimal amounts, but at times which are singular with respect to calendar time. We consider a number of illustrative examples involving CRRA and CARA utility, stocks, and portfolios of options with different strikes, and a model where the act of exercising has an impact on the underlying asset price.

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Section: A Portfolio Of Options With Different Strikesmentioning

confidence: 92%

“…The case with identical options and exponential utility is studied in Henderson and Hobson (2008). Equation (4.6) can be solved by considering the inverse function H = h −1 , so that dH/dz = −(k 1 (1 + δ) + (1 − δ)z)/(γ z(z − k 1 ) 2 ).…”

Section: A Portfolio Of Options With Different Strikesmentioning

confidence: 99%

Optimal Liquidation of Derivative Portfolios

Henderson

Hobson

2011

Mathematical Finance

Self Cite

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“…can be solved by considering the inverse function H = h −1 , so that dH / dz =−( k 1 (1 +δ) + (1 −δ) z )/(γ z ( z − k 1 ) 2 ). It is easily verified (see Henderson and Hobson 2008, for details) that in the case δ≤ 1, h (0) =∞ and The case δ > 1 is similar except that h (0) = k 1 δ/(δ− 1) < ∞ and then H must be modified by a constant to allow for the new boundary condition. We find …”

Section: Examplesmentioning

confidence: 96%

“…From () we can conclude that for ϕ < θ 1 the optimal h solves The case with identical options and exponential utility is studied in Henderson and Hobson (2008). can be solved by considering the inverse function H = h −1 , so that dH / dz =−( k 1 (1 +δ) + (1 −δ) z )/(γ z ( z − k 1 ) 2 ).…”

Section: Examplesmentioning

confidence: 99%

“…The solution is such that the agent waits for a higher asset price before exercising the low strike options than an agent with a portfolio containing the same total quantity of options but each with the same low strike. Henderson and Hobson (2008) previously considered a special case of this example with identical options, exponential utility, and lognormal price dynamics.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Liquidation of Derivative Portfolios

Henderson

Hobson

2010

Mathematical Finance

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We consider the problem facing a risk averse agent who seeks to liquidate or exercise a portfolio of (infinitely divisible) perpetual American style options on a single underlying asset. The optimal liquidation strategy is of threshold form and can be characterized explicitly as the solution of a calculus of variations problem. Apart from a possible initial exercise of a tranche of options, the optimal behavior involves liquidating the portfolio in infinitesimal amounts, but at times which are singular with respect to calendar time. We consider a number of illustrative examples involving CRRA and CARA utility, stocks, and portfolios of options with different strikes, and a model where the act of exercising has an impact on the underlying asset price.

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Optimal exercise of American put options near maturity: A new economic perspective

et al. 2021

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The critical price $$S^{*}\left( t\right) $$ S ∗ t of an American put option is the underlying stock price level that triggers its immediate optimal exercise. We provide a new perspective on the determination of the critical price near the option maturity T when the jump-adjusted dividend yield of the underlying stock is either greater than or weakly smaller than the riskfree rate. Firstly, we prove that $$S^{*}\left( t\right) $$ S ∗ t coincides with the critical price of the covered American put (a portfolio that is long in the put as well as in the stock). Secondly, we show that the stock price that represents the indifference point between exercising the covered put and waiting until T is the European-put critical price, at which the European put is worth its intrinsic value. Finally, we prove that the indifference point’s behavior at T equals $$S^{*}\left( t\right) $$ S ∗ t ’s behavior at T when the stock price is either a geometric Brownian motion or a jump-diffusion. Our results provide a thorough economic analysis of $$S^{*}\left( t\right) $$ S ∗ t and rigorously show the correspondence of an American option problem to an easier European option problem at maturity .

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Perpetual American options in incomplete markets: the infinitely divisible case

Cited by 6 publications

References 17 publications

Optimal Liquidation of Derivative Portfolios

Optimal Liquidation of Derivative Portfolios

Optimal Liquidation of Derivative Portfolios

Optimal exercise of American put options near maturity: A new economic perspective

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