E. Eberlein - Independent Researcher (original) (raw)
Papers by E. Eberlein
Capital requirements, and taxpayer put option values for the major US banks
Assets excluding cash plus short term investments and liabilities less debt are modeled as expone... more Assets excluding cash plus short term investments and liabilities less debt are modeled as exponentials of two Lévy processes. The two Lévy processes are modeled as linear mixtures of four independent Lévy factors. Two of these factors drive assets and liabilities with positive correlations while two of them induce negative correlations. Equity is then a call op- tion on the spread of assets over liabilities. We employ recently developed methods by Hurd and Zhou (2009) to value these spread options using a two dimensional Fourier inversion. The reserve capital required by the taxpayer is determined by making the aggregate risk acceptable to the gen- eral external economy at stress level 0:75 for the distortion minmaxvar: The compound spread option model is calibrated to equity option data at market close on year end to identify the joint law of risky assets and liabilities. We …nd GS and MS to have su¢ cient reserve capital while the other four banks studied are undercapitalized for...
SSRN Electronic Journal, 2010
Decomposition of the balance sheet Cash + Risky Assets = Equity + Risky Debt + Risky Liabilities ... more Decomposition of the balance sheet Cash + Risky Assets = Equity + Risky Debt + Risky Liabilities M(t) + A(t) = J(t) + D(t) + L(t) M(t): Cash + short term investments (cash equivalent reserve) relatively nonrandom: M(t) = Me rt L(t): Short positions in stocks Negative side of a swap contract Payouts on writing credit protections Payouts on selling options Short positions in variance swaps −→ potentially unbounded Net Asset Value Process Calibration Results Required Reserve Capital c Eberlein, Uni Freiburg, 6
When …rms access unbounded liability exposures and are granted limited liability, then an all equ... more When …rms access unbounded liability exposures and are granted limited liability, then an all equity …rm holds a call option, whereby it receives a free option to put losses back to the taxpayers. We call this option the taxpayer put, where the strike is the negative of the level of reserve capital at stake in the …rm. We contribute by (i) valuing this taxpayer put, and (ii) determining the level for reserve capital without a reference to ratings. Reserve capital levels are designed to mitigate the adverse incentives for unnecessary risk introduced by the taxpayer put at the …rm level. In our approach, the level of reserve capital is set to make the aggregate risk of the …rm externally acceptable, where the speci…c form of acceptability employed is positive expectation under a concave distortion of the cash ‡ow distribution. It is observed that in the presence of the taxpayer put, debt holders may not be relied upon to monitor risk as their interests are partially aligned with equity holders by participating in the taxpayer put. Furthermore, the taxpayer put leads to an equity pricing model associated with a market discipline that punishes perceived cash shortfalls.
The Journal of Business, 1998
We investigate a new basic model for asset pricing, the hyperbolic model, which allows an almost ... more We investigate a new basic model for asset pricing, the hyperbolic model, which allows an almost perfect statistical t of stock return data. After a brief introduction into the theory supported by an appendix we use also secondary market data to compare the hyperbolic model to the classical Black-Scholes model. We study implicit volatilities, the smile e ect and the pricing performance. Exploiting the full power of the hyperbolic model, we construct an option value process from a statistical point of view by estimating the implicit risk-neutral density function from option data. Finally we present some new valueat-risk calculations leading to new perspectives to cope with model risk.
Epidemiology of infections due to multiresistantEnterobacter aerogenes in a University Hospital
European Journal of Clinical Microbiology & Infectious Diseases, 1996
Finance and Stochastics, 2005
Limit Laws for Generalizations of Martingales
Dependence in Probability and Statistics, 1986
Given a sequence of random variables (xk)k ≧ 1 one of the important problems in probability and s... more Given a sequence of random variables (xk)k ≧ 1 one of the important problems in probability and statistics is the description of the asymptotic properties of the partial sum process S(t) = Σk ≦ t xk. Essentially three types of results are known: strong laws of large numbers (SLLNs), central limit theorems (CLTs) and laws of the iterated logarithm (LILs). All three of them as well as a number of refinements such as the functional versions of the last two or upper and lower class results can be derived from a strong or almost sure approximation of the partial sum process by a Brownian motion (X(t))t ≧ 0. Since as is well known Brownian motion satisfies all laws, the same holds for the partial sum process if the approximation is sharp enough, namely if (1) for some K > O. In other words formula (1) — once it is established — contains all information on the asymptotic behavior of the partial sums in a very compact form. Thus the question is to look for assumptions under which (1) holds.
SSRN Electronic Journal, 2011
The Sato process model for option prices is expanded to accomodate credit considerations by incor... more The Sato process model for option prices is expanded to accomodate credit considerations by incorporating a single jump to default occuring at an independent random time with a Weibull distribution. Explicit formulas, in this context, for the bid and ask prices of two price economies that price residual risks to levels of risk acceptability are then derived. Liquidity considerations are thereby captured by the movements in the two prices that indirectly re ‡ect changes occuring in the underlying set of zero cost risky cash ‡ows acceptable to the market. In such two price economies it has been proposed that capital requirements supporting a trade are to be set at the di¤erence between the ask and bid prices of the two price economy. We proceed to evaluate the variations in the level of such required capital over time. In particular we observe that the Lehman bankruptcy was primarily a liquidity event for the remaining banks from the perspective of changes in the levels of such a required capital. Additionally, we observe that variations in such capital requirements over time are primarily explained by movements in the option surface and the levels of liquidity, with credit variations playing a part occasionally. The estimations Dilip Madan acknowledges support from the Humboldt foundation as a Research Award Winner.
Mathematics – Key Technology for the Future, 2008
Lévy driven term structure models and cap-floor symmetries
Mathematical Finance, 2012
Both Sides of the Fence
The Lancet, 1978
In this age of modern era, the use of internet must be maximized. Yeah, internet will help us ver... more In this age of modern era, the use of internet must be maximized. Yeah, internet will help us very much not only for important thing but also for daily activities. Many people now, from any level can use internet. The sources of internet connection can also be enjoyed in many places. As one of the benefits is to get the on-line both sides of the fence book, as the world window, as many people suggest.
Journal of Multivariate Analysis, 1989
We study sufficient conditions under which a sequence of stochastic processes W'(f)Lao can be app... more We study sufficient conditions under which a sequence of stochastic processes W'(f)Lao can be approximated almost surely by another sequence of stochastic processes (Y(t))lro. Two different approaches are discussed.
Standard models fail to reproduce observed prices of vanilla options because implied volatilities... more Standard models fail to reproduce observed prices of vanilla options because implied volatilities exhibit a term structure of smiles. We consider time-inhomogeneous Lévy processes to overcome these limitations. Then the scope of this paper is twofold. On the one hand, we apply measure changes in the spirit of Geman et al., to simplify the valuation problem for various options. On the other hand, we discuss a method for the valuation of European options and survey valuation methods for exotic options in Lévy models.
Applied Mathematical Finance, 2010
Index option pricing on world market indices are investigated using Lévy processes with no positi... more Index option pricing on world market indices are investigated using Lévy processes with no positive jumps. Economically this is motivated by the possible absence of longer horizon short positions while mathematically we are able to evaluate for such processes the probability of a Rally Before a Crash (RBC). Three models are used to e¤ectively calibrate index options at an annual maturity and it is observed that positive jumps may be needed for FTSE, N225 and HSI. RBC probabilities are shown to have fallen by 10 points after July 2007. Typical implied volatility curves for such models are also described and illustrated. They have smirks and never smile.
Annals of Finance, 2014
Static and discrete time pricing operators for two price economies are reviewed and then generali... more Static and discrete time pricing operators for two price economies are reviewed and then generalized to the continuous time setting of an underlying Hunt process. The continuous time operators de…ne nonlinear partial integro-di¤erential equations that are solved numerically for the three valuations of bid, ask and expectation. The operators employ concave distortions by inducing a probability into the in…nitesimal generator of a Hunt process. This probability is then distorted. Two nonlinear operators based on di¤erent approaches to truncating small jumps are developed and termed QV for quadratic variation and N L for normalized Lévy. Examples illustrate the resulting valuations. A sample book of derivatives on a single underlier is employed to display the gap between the bid and ask values for the book and the sum of comparable values for the components of the book.
Exact pricing formulae for caps and swaptions in a Lévy term structure model
The Journal of Computational Finance
... Ana-lytical formulae that can be evaluated fast are derived. ... Each caplet is equivalent to... more ... Ana-lytical formulae that can be evaluated fast are derived. ... Each caplet is equivalent to a put option on a zero coupon bond, each floorlet can be considered as a call option (see eg James and Webber (2000, 3.1.5)). Thus, if we derive suitable formulae for calls and puts on zero ...
The Generalized Hyperbolic Model: Financial Derivatives and Risk Measures
Springer Finance, 2002
Statistical analysis of data from the financial markets shows that generalized hyperbolic(GH) dis... more Statistical analysis of data from the financial markets shows that generalized hyperbolic(GH) distributions allow a more realistic description of asset returns than the classicalnormal distribution. GH distributions contain as sub-classes hyperbolic as well asnormal inverse Gaussian (NIG) distributions which have recently been proposed as basicingredients for the modelling of price processes. We derive an option pricing formula forGH driven models
The Distribution of Returns at Longer Horizons
Recent Advances in Financial Engineering 2010 - Proceedings of the KIER-TMU International Workshop on Financial Engineering 2010, 2011
Capital requirements, and taxpayer put option values for the major US banks
Assets excluding cash plus short term investments and liabilities less debt are modeled as expone... more Assets excluding cash plus short term investments and liabilities less debt are modeled as exponentials of two Lévy processes. The two Lévy processes are modeled as linear mixtures of four independent Lévy factors. Two of these factors drive assets and liabilities with positive correlations while two of them induce negative correlations. Equity is then a call op- tion on the spread of assets over liabilities. We employ recently developed methods by Hurd and Zhou (2009) to value these spread options using a two dimensional Fourier inversion. The reserve capital required by the taxpayer is determined by making the aggregate risk acceptable to the gen- eral external economy at stress level 0:75 for the distortion minmaxvar: The compound spread option model is calibrated to equity option data at market close on year end to identify the joint law of risky assets and liabilities. We …nd GS and MS to have su¢ cient reserve capital while the other four banks studied are undercapitalized for...
SSRN Electronic Journal, 2010
Decomposition of the balance sheet Cash + Risky Assets = Equity + Risky Debt + Risky Liabilities ... more Decomposition of the balance sheet Cash + Risky Assets = Equity + Risky Debt + Risky Liabilities M(t) + A(t) = J(t) + D(t) + L(t) M(t): Cash + short term investments (cash equivalent reserve) relatively nonrandom: M(t) = Me rt L(t): Short positions in stocks Negative side of a swap contract Payouts on writing credit protections Payouts on selling options Short positions in variance swaps −→ potentially unbounded Net Asset Value Process Calibration Results Required Reserve Capital c Eberlein, Uni Freiburg, 6
When …rms access unbounded liability exposures and are granted limited liability, then an all equ... more When …rms access unbounded liability exposures and are granted limited liability, then an all equity …rm holds a call option, whereby it receives a free option to put losses back to the taxpayers. We call this option the taxpayer put, where the strike is the negative of the level of reserve capital at stake in the …rm. We contribute by (i) valuing this taxpayer put, and (ii) determining the level for reserve capital without a reference to ratings. Reserve capital levels are designed to mitigate the adverse incentives for unnecessary risk introduced by the taxpayer put at the …rm level. In our approach, the level of reserve capital is set to make the aggregate risk of the …rm externally acceptable, where the speci…c form of acceptability employed is positive expectation under a concave distortion of the cash ‡ow distribution. It is observed that in the presence of the taxpayer put, debt holders may not be relied upon to monitor risk as their interests are partially aligned with equity holders by participating in the taxpayer put. Furthermore, the taxpayer put leads to an equity pricing model associated with a market discipline that punishes perceived cash shortfalls.
The Journal of Business, 1998
We investigate a new basic model for asset pricing, the hyperbolic model, which allows an almost ... more We investigate a new basic model for asset pricing, the hyperbolic model, which allows an almost perfect statistical t of stock return data. After a brief introduction into the theory supported by an appendix we use also secondary market data to compare the hyperbolic model to the classical Black-Scholes model. We study implicit volatilities, the smile e ect and the pricing performance. Exploiting the full power of the hyperbolic model, we construct an option value process from a statistical point of view by estimating the implicit risk-neutral density function from option data. Finally we present some new valueat-risk calculations leading to new perspectives to cope with model risk.
Epidemiology of infections due to multiresistantEnterobacter aerogenes in a University Hospital
European Journal of Clinical Microbiology & Infectious Diseases, 1996
Finance and Stochastics, 2005
Limit Laws for Generalizations of Martingales
Dependence in Probability and Statistics, 1986
Given a sequence of random variables (xk)k ≧ 1 one of the important problems in probability and s... more Given a sequence of random variables (xk)k ≧ 1 one of the important problems in probability and statistics is the description of the asymptotic properties of the partial sum process S(t) = Σk ≦ t xk. Essentially three types of results are known: strong laws of large numbers (SLLNs), central limit theorems (CLTs) and laws of the iterated logarithm (LILs). All three of them as well as a number of refinements such as the functional versions of the last two or upper and lower class results can be derived from a strong or almost sure approximation of the partial sum process by a Brownian motion (X(t))t ≧ 0. Since as is well known Brownian motion satisfies all laws, the same holds for the partial sum process if the approximation is sharp enough, namely if (1) for some K > O. In other words formula (1) — once it is established — contains all information on the asymptotic behavior of the partial sums in a very compact form. Thus the question is to look for assumptions under which (1) holds.
SSRN Electronic Journal, 2011
The Sato process model for option prices is expanded to accomodate credit considerations by incor... more The Sato process model for option prices is expanded to accomodate credit considerations by incorporating a single jump to default occuring at an independent random time with a Weibull distribution. Explicit formulas, in this context, for the bid and ask prices of two price economies that price residual risks to levels of risk acceptability are then derived. Liquidity considerations are thereby captured by the movements in the two prices that indirectly re ‡ect changes occuring in the underlying set of zero cost risky cash ‡ows acceptable to the market. In such two price economies it has been proposed that capital requirements supporting a trade are to be set at the di¤erence between the ask and bid prices of the two price economy. We proceed to evaluate the variations in the level of such required capital over time. In particular we observe that the Lehman bankruptcy was primarily a liquidity event for the remaining banks from the perspective of changes in the levels of such a required capital. Additionally, we observe that variations in such capital requirements over time are primarily explained by movements in the option surface and the levels of liquidity, with credit variations playing a part occasionally. The estimations Dilip Madan acknowledges support from the Humboldt foundation as a Research Award Winner.
Mathematics – Key Technology for the Future, 2008
Lévy driven term structure models and cap-floor symmetries
Mathematical Finance, 2012
Both Sides of the Fence
The Lancet, 1978
In this age of modern era, the use of internet must be maximized. Yeah, internet will help us ver... more In this age of modern era, the use of internet must be maximized. Yeah, internet will help us very much not only for important thing but also for daily activities. Many people now, from any level can use internet. The sources of internet connection can also be enjoyed in many places. As one of the benefits is to get the on-line both sides of the fence book, as the world window, as many people suggest.
Journal of Multivariate Analysis, 1989
We study sufficient conditions under which a sequence of stochastic processes W'(f)Lao can be app... more We study sufficient conditions under which a sequence of stochastic processes W'(f)Lao can be approximated almost surely by another sequence of stochastic processes (Y(t))lro. Two different approaches are discussed.
Standard models fail to reproduce observed prices of vanilla options because implied volatilities... more Standard models fail to reproduce observed prices of vanilla options because implied volatilities exhibit a term structure of smiles. We consider time-inhomogeneous Lévy processes to overcome these limitations. Then the scope of this paper is twofold. On the one hand, we apply measure changes in the spirit of Geman et al., to simplify the valuation problem for various options. On the other hand, we discuss a method for the valuation of European options and survey valuation methods for exotic options in Lévy models.
Applied Mathematical Finance, 2010
Index option pricing on world market indices are investigated using Lévy processes with no positi... more Index option pricing on world market indices are investigated using Lévy processes with no positive jumps. Economically this is motivated by the possible absence of longer horizon short positions while mathematically we are able to evaluate for such processes the probability of a Rally Before a Crash (RBC). Three models are used to e¤ectively calibrate index options at an annual maturity and it is observed that positive jumps may be needed for FTSE, N225 and HSI. RBC probabilities are shown to have fallen by 10 points after July 2007. Typical implied volatility curves for such models are also described and illustrated. They have smirks and never smile.
Annals of Finance, 2014
Static and discrete time pricing operators for two price economies are reviewed and then generali... more Static and discrete time pricing operators for two price economies are reviewed and then generalized to the continuous time setting of an underlying Hunt process. The continuous time operators de…ne nonlinear partial integro-di¤erential equations that are solved numerically for the three valuations of bid, ask and expectation. The operators employ concave distortions by inducing a probability into the in…nitesimal generator of a Hunt process. This probability is then distorted. Two nonlinear operators based on di¤erent approaches to truncating small jumps are developed and termed QV for quadratic variation and N L for normalized Lévy. Examples illustrate the resulting valuations. A sample book of derivatives on a single underlier is employed to display the gap between the bid and ask values for the book and the sum of comparable values for the components of the book.
Exact pricing formulae for caps and swaptions in a Lévy term structure model
The Journal of Computational Finance
... Ana-lytical formulae that can be evaluated fast are derived. ... Each caplet is equivalent to... more ... Ana-lytical formulae that can be evaluated fast are derived. ... Each caplet is equivalent to a put option on a zero coupon bond, each floorlet can be considered as a call option (see eg James and Webber (2000, 3.1.5)). Thus, if we derive suitable formulae for calls and puts on zero ...
The Generalized Hyperbolic Model: Financial Derivatives and Risk Measures
Springer Finance, 2002
Statistical analysis of data from the financial markets shows that generalized hyperbolic(GH) dis... more Statistical analysis of data from the financial markets shows that generalized hyperbolic(GH) distributions allow a more realistic description of asset returns than the classicalnormal distribution. GH distributions contain as sub-classes hyperbolic as well asnormal inverse Gaussian (NIG) distributions which have recently been proposed as basicingredients for the modelling of price processes. We derive an option pricing formula forGH driven models
The Distribution of Returns at Longer Horizons
Recent Advances in Financial Engineering 2010 - Proceedings of the KIER-TMU International Workshop on Financial Engineering 2010, 2011