Results 1  10
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14
A Continuity Correction For Discrete Barrier Options
 Mathematical Finance
, 1997
"... this paper, we introduce a simple continuity correction for approximate pricing of discrete barrier options. Our method uses formulas for the prices of continuous barrier options but shifts the barrier to correct for discrete monitoring. The shift is determined solely by the monitoring frequency, th ..."
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Cited by 39 (5 self)
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this paper, we introduce a simple continuity correction for approximate pricing of discrete barrier options. Our method uses formulas for the prices of continuous barrier options but shifts the barrier to correct for discrete monitoring. The shift is determined solely by the monitoring frequency, the asset volatility, and a constant # # 0.5826. It is therefore trivial to implement. Compared with using the unadjusted continuous price, our formula reduces the error from O(1/ # m) to o(1/ # m), as the number of monitoring points m increases. Numerical results indicate that the approximation is accurate enough to correctly price barrier options in all but the most extreme circumstance; i.e., except when the price of the underlying asset nearly coincides with the barrier. Our analysis is based on the usual BlackScholes market assumptions (Black and Scholes 1973). In particular, the asset price {S t , t # 0} follows the stochastic differential equation dS S =#dt +# dZ, (1.1) where Z is a standard Wiener process, # and #>0 are constants, and S 0 is fixed. The term structure is flat, and we let r denote the constant, continuously compounded riskfree interest rate. The price of a claim contingent on S is the expected present value of its cash flows under the equivalent martingale measure, which sets # = r in (1.1). Let H denote the level of the barrier. An up option has H > S 0 and a down option has H < S 0 ; in particular, we always assume H #= S 0 . The asset price reaches the barrier for the first time at 2 # H = inf{t > 0:S t =H}; (1.2) this is an upcrossing if S 0 < H and a downcrossing if S 0 > H.Aknockin call option with maturity T and strike K pays (S T  K ) + at time T if # H # T and zero otherwise. Its price is thus 3 e rT E[(S T K) + ...
The Russian Option: Reduced Regret
, 1993
"... this paper the value of the option (i.e. the supremum in (1.2)) will be found exactly, and in particular it will be shown that the maximum in (1.2) is finite if and only if r ? ¯ : (1.4) Assuming (1.4), an explicit formula is given for both the maximal expected present value and the optimal stopping ..."
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Cited by 36 (2 self)
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this paper the value of the option (i.e. the supremum in (1.2)) will be found exactly, and in particular it will be shown that the maximum in (1.2) is finite if and only if r ? ¯ : (1.4) Assuming (1.4), an explicit formula is given for both the maximal expected present value and the optimal stopping rule in (2.4), which is not a fixed time rule but depends heavily on the observed values of X t and S t . We call the financial option described above a "Russian option" for two reasons. First, this name serves to (facetiously) differentiate it from American and European options, which have been extensively studied in financial economics, especially with the new interest in market economics in Russia. Second, our solution of the stopping problem (1.2) is derived by the socalled principle of smooth fit, first enunciated by the great Russian mathematician, A. N. Kolmogorov, cf. [4, 5]. The Russian option is characterized by "reduced regret" because the owner is paid the maximum stock price up to the time of exercise and hence feels less remorse at not having exercised at the maximum. For purposes of comparison and to emphasize the mathematical nature of the contribution here, we conclude the paper by analyzing an optimal stopping problem for the Russian option based on Bachelier's (1900) original linear model of stock price fluctuations, X
Connecting Discrete and Continuous PathDependent Options
, 1999
"... . This paper develops methods for relating the prices of discrete and continuoustime versions of pathdependent options sensitive to extremal values of the underlying asset, including lookback, barrier, and hindsight options. The relationships take the form of correction terms that can be interpre ..."
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Cited by 27 (3 self)
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. This paper develops methods for relating the prices of discrete and continuoustime versions of pathdependent options sensitive to extremal values of the underlying asset, including lookback, barrier, and hindsight options. The relationships take the form of correction terms that can be interpreted as shifting a barrier, a strike, or an extremal price. These correction terms enable us to use closedform solutions for continuous option prices to approximate their discrete counterparts. We also develop discretetime discretestate lattice methods for determining accurate prices of discrete and continuous pathdependent options. In several cases, the lattice methods use correction terms based on the connection between discrete and continuoustime prices which dramatically improve convergence to the accurate price. Key words: Barrier options, lookback options, continuity corrections, trinomial trees JEL classification: G13, C63, G12 Mathematics Subject Classification (1991): 90A09, 60J15, 65N06 1
Ladder Heights, Gaussian Random Walks, and the Riemann Zeta Function
 Ann. Probab
, 1996
"... this paper is the behavior of E ` S near ..."
Inside Information And Stock Fluctuations
, 1999
"... A model of an incomplete market with the incorporation of a new notion of "inside information" is posed. The usual assumption that the stock price is Markovian is modified by adjoining a hidden Markov process to the BlackScholes exponential Brownian motion model for stock fluctuations. The drift ..."
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Cited by 8 (4 self)
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A model of an incomplete market with the incorporation of a new notion of "inside information" is posed. The usual assumption that the stock price is Markovian is modified by adjoining a hidden Markov process to the BlackScholes exponential Brownian motion model for stock fluctuations. The drift and volatility parameters take different values when the hidden Markov process is in different states. For example, it is 0 when there is no subset of the market which has or which believes it has, extra information. However, the hidden process is in state 1 when information is not equally shared by all, and then the behavior of the members in the subset causes increased fluctuations in the stock price. This model
An optimal strategy for sellers in an online auction
 ACM Trans. Internet Tech
"... We consider an online auction setting where the seller attempts to sell an item. Bids arrive over time and the seller has to make an instant decision to either accept this bid and close the auction or reject it and move on to the next bid, with the hope of higher gains. What should be the seller’s s ..."
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Cited by 6 (0 self)
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We consider an online auction setting where the seller attempts to sell an item. Bids arrive over time and the seller has to make an instant decision to either accept this bid and close the auction or reject it and move on to the next bid, with the hope of higher gains. What should be the seller’s strategy to maximize gains? Using techniques from convex analysis, we provide an explicit closedform optimal solution (and hence a simple optimum online algorithm) for the seller. Our methodology is attractive to online auction systems that have to make an instant decision, especially when it is not humanly possible to evaluate each bid individually, when the number of bids is large or unknown ahead of time, and when the bidders are unwilling to wait.
Option Pricing in a World With Arbitrage
, 2000
"... We discuss option pricing problems under a new model of stock fluctuations. This model captures the information distribution among investors by adjoining a hidden Markov process to the BlackScholes exponential Brownian motion model. We provide new valuations for various standard hedge options, s ..."
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We discuss option pricing problems under a new model of stock fluctuations. This model captures the information distribution among investors by adjoining a hidden Markov process to the BlackScholes exponential Brownian motion model. We provide new valuations for various standard hedge options, such as European, perpetual American and lookback options.
List of papers................................................................................................................................... vii
"... Denmark Denne afhandling er, i forbindelse med de nedenfor anførte, tidligere offentliggjorte afhandlinger, af Det naturvidenskabelige Fakultet ved Aarhus Universitet antaget til forsvar for den naturvidenskabelige doktorgrad. Forsvarshandlingen finder sted fredag den 12. april 2002 kl. 13.15 i Audi ..."
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Denmark Denne afhandling er, i forbindelse med de nedenfor anførte, tidligere offentliggjorte afhandlinger, af Det naturvidenskabelige Fakultet ved Aarhus Universitet antaget til forsvar for den naturvidenskabelige doktorgrad. Forsvarshandlingen finder sted fredag den 12. april 2002 kl. 13.15 i Auditorium F p˚a Institut for Matematiske Fag, Aarhus Universitet.