scholarly journals Discrete sums of geometric Brownian motions, annuities and Asian options

2016 ◽  
Vol 70 ◽  
pp. 19-37 ◽  
Author(s):  
Dan Pirjol ◽  
Lingjiong Zhu
Keyword(s):  
Asian Options ◽  
Brownian Motions ◽  
Geometric Brownian Motions

CMBS Tranche Valuation Framework: Correlated Geometric Brownian Motions Simulation

2011 ◽  
Vol 21 (1) ◽  
pp. 55-66 ◽  
Author(s):  
Peijie Shiu ◽  
Uyen Luong ◽  
Yadin Rozov
Keyword(s):  
Brownian Motions ◽  
Geometric Brownian Motions

scholarly journals PRICING OF CONTINGENT CLAIMS IN A TWO-DIMENSIONAL MODEL WITH RANDOM DIVIDENDS

2009 ◽  
Vol 12 (08) ◽  
pp. 1091-1104 ◽  
Author(s):  
PAVEL V. GAPEEV ◽  
MONIQUE JEANBLANC
Keyword(s):  
Financial Market ◽  
Diffusion Processes ◽  
Partial Information ◽  
Asset Price ◽  
Contingent Claims ◽  
Dimensional Model ◽  
Random Drift ◽  
Brownian Motions ◽  
Risky Assets ◽  
Geometric Brownian Motions

We study a model of a financial market in which two risky assets are paying dividends with rates changing their initial values to other constant ones when certain events occur. Such events are associated with the first times at which the value processes of issuing firms, modeled by geometric Brownian motions, fall to some prescribed levels. The asset price dynamics are described by exponential diffusion processes with random drift rates and independent driving Brownian motions. We derive closed form expressions for rational values of European contingent claims, under full and partial information.

PRICING AND FILTERING IN A TWO-DIMENSIONAL DIVIDEND SWITCHING MODEL

2010 ◽  
Vol 13 (07) ◽  
pp. 1001-1017 ◽  
Author(s):  
PAVEL V. GAPEEV ◽  
MONIQUE JEANBLANC
Keyword(s):  
Asset Price ◽  
Contingent Claims ◽  
Conditional Probability Density ◽  
Random Drift ◽  
Brownian Motions ◽  
Risky Assets ◽  
Switching Model ◽  
The Times ◽  
Geometric Brownian Motions ◽  
Random Times

We study a model of a financial market in which the dividend rates of two risky assets change their initial values to other constant ones at the times at which certain unobservable external events occur. The asset price dynamics are described by geometric Brownian motions with random drift rates switching at exponential random times, that are independent of each other and the constantly correlated driving Brownian motions. We obtain closed form expressions for the rational values of European contingent claims through the filtering estimates of occurrence of the switching times and their conditional probability density derived given the filtration generated by the underlying asset price processes.

MAXIMIZING THE PROBABILITY OF A PERFECT HEDGE USING AN IMPERFECTLY CORRELATED INSTRUMENT

2005 ◽  
Vol 08 (06) ◽  
pp. 763-789 ◽  
Author(s):  
DAVID HOBSON ◽  
JEREMY PENN
Keyword(s):  
Time Horizon ◽  
Fixed Time ◽  
Contingent Claim ◽  
Brownian Motions ◽  
Quantile Hedging ◽  
Terminal Wealth ◽  
Hedging Problem ◽  
Geometric Brownian Motions ◽  
The Impact ◽  
Concrete Model

Let Xϕ denote the trading wealth generated using a strategy ϕ, and let CT be a contingent claim which is not spanned by the traded assets. Consider the problem of finding the strategy which maximizes the probability of terminal wealth meeting or exceeding the claim value at some fixed time horizon, i.e., of finding [Formula: see text]. This problem is sometimes referred to as the quantile hedging problem. We consider the quantile hedging problem when the traded asset and the contingent claim are correlated geometric Brownian motions. This fits with several important examples. One of the benefits of working with such a concrete model is that although it is incomplete we can still do calculations. In particular, we can consider some detailed issues such as the impact of the timing at which information about CT is revealed.

ON BOUNCING GEOMETRIC BROWNIAN MOTIONS

2018 ◽  
Vol 33 (4) ◽  
pp. 591-617
Author(s):  
Xin Liu ◽  
Vidyadhar G. Kulkarni ◽  
Qi Gong
Keyword(s):  
Brownian Motion ◽  
Standard Brownian Motion ◽  
Prediction Formula ◽  
Limit Order ◽  
Brownian Motions ◽  
Meeting Point ◽  
Order Books ◽  
Geometric Brownian Motions ◽  
Limit Order Books

A pair of bouncing geometric Brownian motions (GBMs) is studied. The bouncing GBMs behave like GBMs except that, when they meet, they bounce off away from each other. The object of interest is the position process, which is defined as the position of the latest meeting point at each time. We study the distributions of the time and position of their meeting points, and show that the suitably scaled logarithmic position process converges weakly to a standard Brownian motion as the bounce size δ→0. We also establish the convergence of the bouncing GBMs to mutually reflected GBMs as δ→0. Finally, applying our model to limit order books, we derive a simple and effective prediction formula for trading prices.

CREDIT DEFAULT SWAPS IN TWO-DIMENSIONAL MODELS WITH VARIOUS INFORMATIONS FLOWS

2020 ◽  
Vol 23 (02) ◽  
pp. 2050010
Author(s):  
PAVEL V. GAPEEV ◽  
MONIQUE JEANBLANC
Keyword(s):  
Financial Market ◽  
Risk Model ◽  
Credit Default Swaps ◽  
Linear Combinations ◽  
Brownian Motions ◽  
No Arbitrage ◽  
Default Intensity ◽  
Credit Default ◽  
Geometric Brownian Motions ◽  
Credit Risk Model

We study a credit risk model of a financial market in which the dynamics of intensity rates of two default times are described by linear combinations of three independent geometric Brownian motions. The dynamics of two default-free risky asset prices are modeled by two geometric Brownian motions which are dependent of the ones describing the default intensity rates. We obtain closed form expressions for the no-arbitrage prices of both risk-free and risky credit default swaps given the reference filtration initially and progressively enlarged by the two default times. The accessible default-free reference filtration is generated by the standard Brownian motions driving the model.

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