### Citations

1657 |
Theory of Rational Option Pricing
- Merton
- 1973
(Show Context)
Citation Context ...f a perpetual American call option with strike price q and interest rate r− γ. It is well-known that if the interest rate is non-negative, then a call option should not be exercised early (see Merton =-=[6]-=-), and the value of the perpetual option coincides with the value of the underlying. The main novelty of the following result in [9] is thus the formulas for γ > r (i.e. for α > 0 in the notation belo... |

355 |
Brownian Motion and Stochastic Calculus, Second Edition
- Karatzas, Shreve
- 1991
(Show Context)
Citation Context ...ll x ≥ q we find that Yt is a martingale for 0 ≤ t < ∞. Recalling our convention that F (X∞) = 0, an application of the Optional Sampling Theorem (see for example Problem 1.3.16 and Theorem 1.3.22 in =-=[4]-=-) shows that F (x) = Y0 ≥ Ex [Yτ ] = Ex [ e−µτF (Xτ ) ] for any stopping time τ ≤ τq. Since F ≥ h, we find that F (x) ≥ sup τ≤τq Ex [ e−µτh(Xτ ) ] = U(x, µ, ε). 6 ERIK EKSTRÖM AND HENRIK WANNTORP To ... |

127 |
Optimal Stopping and Free-Boundary Problems
- Peskir, Shiryaev
- 2006
(Show Context)
Citation Context ...ing of Theorem 3.1 in which there is no optimal stopping time. For a general discussion on the connection between optimal stopping problems and free boundary problems we refer to the recent monograph =-=[6]-=-. Proof. First note that the function f(y) = (1− ε/q)y − 2µ 2µ+ σ2 − σ2 2µ+ σ2 y1+2µ/σ 2 (12) grows linearly for large y, is convex, and satisfies f(1) = −ε/q (and if ε = 0, then f ′(1) = 0). This pro... |

20 | A barrier option of American type
- KARATZAS, WANG
- 2000
(Show Context)
Citation Context ...ibe the optimal exercise time in cases when it exists. The analysis of this barrier option seems to be new in the literature, and may be of independent interest. For a study of a related problem, see =-=[5]-=-. To formulate the problem, let X solve dXt = µXt dt + σXt dWt, where µ ∈ R is a constant and W is a Brownian motion. For q > 0, let τq = inf{t ≥ 0 : Xt ≤ q} MARGIN CALL STOCK LOANS 5 be the first pas... |

11 |
Arbitrage Theory in Continuous Time, second edn., Oxford Finance
- Björk
- 2004
(Show Context)
Citation Context ...at we specify the stock dynamics directly under the pricing measure, so there is no need to change the measure when pricing options on S. Thus, according to standard arbitrage theory (see for example =-=[2]-=-), the value of a non-recourse stock loan is V 0(x, q) = sup τ Ex [ e−rτ (Sτ − qe γτ )+ ] , (2) where the index indicates that S0 = x and the supremum is taken over stopping times. Here and throughout... |

10 | On the properties of r-excessive mappings for a class of diffusions - Alvarez - 2003 |

3 |
Stock loans
- Xia, Zhou
- 2007
(Show Context)
Citation Context ...ercise time. Moreover, we provide a sensitivity analysis of the loan value with respect to the model parameters. 1. Introduction Recently, Xia and Zhou studied perpetual non-recourse stock loans, see =-=[8]-=-. These are contracts in which the holder borrows money with a stock as collateral. The holder may at any instant choose to pay back the loan and when doing so, he retrieves the stock and the contract... |

1 |
The generalized perpetual American exchange-option problem
- Wong
- 2008
(Show Context)
Citation Context ...he valuation of a non-recourse stock loan reduces to the valuation of an American call option with a negative interest rate, and the optimal exercise strategy is described. For related work, see also =-=[7]-=- in which an exchange option is studied in an economy with negative interest rate. In reality, many stock loans are equipped with the additional feature that the lender may issue a margin call in case... |