Monte Carlo valuation of American options

By L. Rogers. 2002

521 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/d556592fae9126550fda1f523ee5dcf2c82646a0

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Citations in the corpus

Sharp Finite-Time Iterated-Logarithm Martingale Concentration (2014, background): “n used to great eﬀect to uniformly bound processes indexed on metric spaces, by using covering arguments which are also sensitive to variation at diﬀerent scales. Second, it has been previously noted [17, 9] that martingale stopping times and uniform concentration are dual, and our technique provide”
Option Pricing Under a Double Exponential Jump Diffusion Model (2004, background): “…(1998), Ju (1998), Geske and Johnson (1984), McMillan (1986), Tilley (1993), Tsitsiklis and van Roy (1999), Sullivan (2000), Broadie and Glasserman (1997), Carriére (1996), Longstaff and Schwartz (2001), Rogers (2002), Haugh and Kogan (2002), and references therein. in the notation of Equation (4).”
Counterparty Risk Valuation: A Marked Branching Diffusion Approach (2012, methodology): “It does not require regressions as in the well-known Longstaff-Schwartz method [10] or a “Monte-Carlo of Monte-Carlo method” as in Rogers’s dual algorithm [1, 14].”
Primal-Dual Simulation Algorithm for Pricing Multidimensional American Options (2004, unknown): “We assume that the financial markets are complete and that the expectation is taken under the risk-neutral measure.2 More generally, the Bermudan option value at time t T is Qt = max ( ht, Et [ Bt Bt+1 Qt+1 ]) .”
DGM: A deep learning algorithm for solving partial differential equations (2017, unknown): “[45] derived that the PDE solution u ( t, x ) lies in the interval: where τ = inf { t ∈ [0 , T ] : f ( t, X t ; θ ) < g ( X t ) } and M s is a martingale constructed from the approximate The bounds (4.6) depend only on the approximation f ( t, x ; θ ), which is known, and can be evaluated via Monte…”
Simulation for American Options: Regression Now or Regression Later? (2004, background): “The bound then follows along the lines in Haugh and Kogan [10] and Rogers [12].”
Gas Storage Valuation Using a Monte Carlo Method (2008, methodology): “We simulate M independent price paths according to the one-factor Schwartz (1997) model with time dependent drift where we use antithetic sampling, see e.”
TRUE UPPER BOUNDS FOR BERMUDAN PRODUCTS VIA NON‐NESTED MONTE CARLO (2009, unknown): “Rogers (2002) and independently Haugh and Kogan (2004) developed a dual method which provides an upper bound for the Bermudan price, given an approximation of the Snell envelope.”
Interpretable Optimal Stopping (2018, background): “Examples include Rogers (2002), Andersen and Broadie (2004), Haugh and Kogan (2004), Chen and Glasserman (2007), Brown et al. (2010) and Desai et al. (2012b).”
A PRIMAL–DUAL ALGORITHM FOR BSDES (2013, methodology): “m as the primal problem, then the pathwise approach can be interpreted as a dual minimization problem in the sense of information relaxation. This type of duality was ﬁrst introduced independently by Rogers (2002) and Haugh and Kogan (2004) in the context of Bermudan option pricing, and was later ex”
A New Learning Algorithm for Optimal Stopping (2009, background): “# ; i = 1; 2;:::;d: ( 27 ) Furthermore, the stationary policy n is optimal if and only if (i) attains the minimum on the right for each i.”
The duality of optimal exercise and domineering claims: a Doob–Meyer decomposition approach to the Snell envelope (2007, unknown): “The martingale part of the Doob–Meyer decomposition of the Snell envelope, as utilized in [8,15,31] furnishes the main example of a domineering claim.”
Pricing American Options: A Duality Approach (2018, background): “…to portfolio optimization problems has proved successful and is now widely used in finance, (see, for example, Karatzas and Shreve 1998), the dual approach to the American option pricing problem does not seem to have been previously developed other than in recent independent work by Rogers (2001).”
Monte Carlo and Quasi-Monte Carlo Sampling (2009, methodology): “Another family of methods that produce high-biased estimators is the dual approach introduced independently in [351] and [153].”
MONTE CARLO METHODS FOR THE VALUATION OF MULTIPLE‐EXERCISE OPTIONS (2004, unknown): “This is an extension of the single-exercise case (n = 1) where the dual problem, found in Haugh and Kogan (2001) and Rogers (2002), is given by V ,10 = infM∈H0 Et [ max 0≤t T (Zt − Mt) ] .”