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Option pricing when underlying stock returns are discontinuous
 Journal of Financial Economics
, 1976
"... The validity of the classic BlackScholes option pricing formula dcpcnds on the capability of investors to follow a dynamic portfolio strategy in the stock that replicates the payoff structure to the option. The critical assumption required for such a strategy to be feasible, is that the underlying ..."
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Cited by 507 (1 self)
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The validity of the classic BlackScholes option pricing formula dcpcnds on the capability of investors to follow a dynamic portfolio strategy in the stock that replicates the payoff structure to the option. The critical assumption required for such a strategy to be feasible, is that the underlying stock return dynamics can be described by a stochastic process with a continuous sample path. In this paper, an option pricing formula is derived for the moregeneral cast when the underlying stock returns are gcncrated by a mixture of both continuous and jump processes. The derived formula has most of the attractive features of the original Black&holes formula in that it does not dcpcnd on investor prcfcrenccs or knowledge of the expcctsd return on the underlying stock. Morcovcr, the same analysis applied to the options can bc extcndcd to the pricingofcorporatc liabilities. 1. Intruduction In their classic paper on the theory of option pricing, Black and Scholcs (1973) prcscnt a mode of an:llysis that has rcvolutionizcd the theory of corporate liability pricing. In part, their approach was a breakthrough because it leads to pricing formulas using. for the most part, only obscrvablc variables. In particular,
Stochastic Volatility for Lévy Processes
, 2001
"... Three processes re°ecting persistence of volatility are initially formulated by evaluating three L¶evy processes at a time change given by the integral of a mean reverting square root process. The model for the mean reverting time change is then generalized to include NonGaussian models that are so ..."
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Cited by 100 (8 self)
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Three processes re°ecting persistence of volatility are initially formulated by evaluating three L¶evy processes at a time change given by the integral of a mean reverting square root process. The model for the mean reverting time change is then generalized to include NonGaussian models that are solutions to OU (OrnsteinUhlenbeck) equations driven by one sided discontinuous L¶evy processes permitting correlation with the stock. Positive stock price processes are obtained by exponentiating and mean correcting these processes, or alternatively by stochastically exponentiating these processes. The characteristic functions for the log price can be used to yield option prices via the fast Fourier transform. In general, mean corrected exponentiation performs better than employing the stochastic exponential. It is observed that the mean corrected exponential model is not a martingale in the ¯ltration in which it is originally de¯ned. This leads us to formulate and investigate the important property of martingale marginals where we seek martingales in altered ¯ltrations consistent with the one dimensional marginal distributions of the level of the process at each future date. 1
Randomization and the American Put
 The Review of Financial Studies
, 1998
"... Conference. In particular, I am grateful to an unknown RFS referee, Kerry Back, Michael Brennan, Darrell Du e, ..."
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Cited by 53 (1 self)
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Conference. In particular, I am grateful to an unknown RFS referee, Kerry Back, Michael Brennan, Darrell Du e,
A Simple Robust Link Between American Puts and Credit Insurance
, 2008
"... We develop a simple robust link between equity outofthemoney American put options and a pure credit insurance contract on the same reference company. Assuming that the stock price stays above a barrier B> 0 before default but drops and remains below a lower barrier A < B after default, we show th ..."
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Cited by 3 (1 self)
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We develop a simple robust link between equity outofthemoney American put options and a pure credit insurance contract on the same reference company. Assuming that the stock price stays above a barrier B> 0 before default but drops and remains below a lower barrier A < B after default, we show that the spread between two coterminal American put options struck within the default corridor [A,B] scaled by their strike difference replicates a standardized credit insurance contract that pays one dollar at default whenever the company defaults prior to the option expiry and zero otherwise. Given the presence of the default corridor, this simple replicating strategy is robust to the details of pre and postdefault stock price dynamics, interest rate movements, and default risk fluctuations. We use quotes on American puts to infer the value of the credit insurance contract and compare it to that estimated from the credit default swap spreads. Collecting data on several companies, we identify strong comovements between the credit insurance values inferred from the two markets. We also find that deviations between the two estimates cannot be fully explained by common variables used for explaining American put values, such as the underlying stock price and stock return volatility, but the crossmarket deviations can predict future movements in American puts.
On the Internal Consistency of the BlackScholes Option Pricing Model
, 2008
"... Abstract: We study the information structure implied by models in which the asset price is always risky and there are no arbitrage opportunities. Using the martingale representation of Harrison and Kreps (1979), a claim takes its value from the stream of discounted expected payments. Equivalently, a ..."
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Abstract: We study the information structure implied by models in which the asset price is always risky and there are no arbitrage opportunities. Using the martingale representation of Harrison and Kreps (1979), a claim takes its value from the stream of discounted expected payments. Equivalently, a pricingkernel is sufficient to value the payment stream. If a price process is always risky, then either the payment or the discount factor must also be continually risky. This observation substantially complicates the valuation of contingent claims. Many classical option pricing formulas abstract from both risky dividends and risky discount rates. In order to value contingent claims, one of the assumptions must be abandoned.
Do RiskTaking Incentives Induce CEOs to Invest? New Evidence from Acquisitions
, 2013
"... This paper examines the effect of risktaking incentives on acquisition investments. We provide evidence that high vega CEOs are more likely to invest in acquisitions. Economically, an interquartile range change in vega translates into an approximately 6% enhancement in acquisition investments. Fur ..."
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This paper examines the effect of risktaking incentives on acquisition investments. We provide evidence that high vega CEOs are more likely to invest in acquisitions. Economically, an interquartile range change in vega translates into an approximately 6% enhancement in acquisition investments. Further, the association between risktaking incentives and acquisition investments is generally not affected by several corporate governance mechanisms. Moreover, risktaking incentives do not promote internal investments. Finally, bidders with high vega CEOs generate relatively larger acquisition announcement returns. Overall, the results are consistent with the theory that high risktaking incentives induce CEOs to undertake investments. JEL Classification: G34; M12
45 ON BECOMING AN ACTUARY OF THE THIRD KIND
"... The growing importance of investment performance in insurance operutions, the increusing volutility in finnnciul markets und the emergence of investmentlinked insurance contructs are creating the need for actuaries to develop new skills and a greater awareness of investment performance. Huns Biihlm ..."
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The growing importance of investment performance in insurance operutions, the increusing volutility in finnnciul markets und the emergence of investmentlinked insurance contructs are creating the need for actuaries to develop new skills and a greater awareness of investment performance. Huns Biihlmann recently classified actuaries that work with the investment side of insurunce as actuaries of the third kind. This paper describes the similarities and differences between actuarial science and financial economics, indicates the current issues in financial economics, and summarizes the mujor applications of fmuncial economics to insurance. 1.