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Author: Stephen E. Satchell Publisher: ISBN: Category : Languages : en Pages : 29
Book Description
This paper assumes that the underlying asset prices are lognormally distributed and drives necessary and sufficient conditions for the valuation of options using a Black-Scholes type methodology. It is shown that the price of a futures-style, market-to-market option is given by Black s formula if the pricing kernel is lognormally distributed. Assuming that this condition is fulfilled, it is then shown that the Black-Scholes formula prices a spot-settled contingent claim, if the interest-rate accumulation factor is lognormally distributed. Otherwise, the Black-Scholes formula holds if the product of the pricing kernel and the interest-rate accumulation factor is lognormally distributed.
Author: Stephen E. Satchell Publisher: ISBN: Category : Languages : en Pages : 29
Book Description
This paper assumes that the underlying asset prices are lognormally distributed and drives necessary and sufficient conditions for the valuation of options using a Black-Scholes type methodology. It is shown that the price of a futures-style, market-to-market option is given by Black s formula if the pricing kernel is lognormally distributed. Assuming that this condition is fulfilled, it is then shown that the Black-Scholes formula prices a spot-settled contingent claim, if the interest-rate accumulation factor is lognormally distributed. Otherwise, the Black-Scholes formula holds if the product of the pricing kernel and the interest-rate accumulation factor is lognormally distributed.
Author: Tobias Herwig Publisher: Springer Science & Business Media ISBN: 3540308385 Category : Business & Economics Languages : en Pages : 112
Book Description
1. 1 The Area of Research In this thesis, we will investigate the 'market-conform' pricing of newly issued contingent claims. A contingent claim is a derivative whose value at any settlement date is determined by the value of one or more other underlying assets, e. g. , forwards, futures, plain-vanilla or exotic options with European or American-style exercise features. Market-conform pricing means that prices of existing actively traded securities are taken as given, and then the set of equivalent martingale measures that are consistent with the initial prices of the traded securities is derived using no-arbitrage arguments. Sometimes in the literature other expressions are used for 'market-conform' valuation - 'smile-consistent' valuation or 'fair-market' valuation - that describe the same basic idea. The seminal work by Black and Scholes (1973) (BS) and Merton (1973) mark a breakthrough in the problem of hedging and pricing contingent claims based on no-arbitrage arguments. Harrison and Kreps (1979) provide a firm mathematical foundation for the Black-Scholes- Merton analysis. They show that the absence of arbitrage is equivalent to the existence of an equivalent martingale measure. Under this mea sure the normalized security price process forms a martingale and so securities can be valued by taking expectations. If the securities market is complete, then the equivalent martingale measure and hence the price of any security are unique.
Author: Bruce Neal Lehmann Publisher: ISBN: Category : Securities Languages : en Pages : 19
Book Description
This paper provides a road map for building a contingent claims theory of limit order markets grounded in a simple observation: limit orders are equivalent to a portfolio of cash-or-nothing and asset-or-nothing digital options on market order flow. However, limit orders are not conventional derivative securities: order flow is an endogenous, non-price state variable; the underlying asset value is a construct, the value of the security in different order flow states; and arbitrage trading or hedging of limit orders is not feasible. Fortunately, none of these problems is fatal since options on order flow can be conceptualized as bets implicit in limit orders, arbitrage trading can be replaced by limit order substitution, and plausible assumptions can be made about the endogeneity of order flow states and their associated asset values. The analysis yields two main results: Arrow-Debreu prices for order flow ''states'' are proportional to the slope of the limit order book and the limit order book at one time proves to be identical to that at an earlier time adjusted for the net order flow since that time when all information arrives via trades.
Author: Angelika Esser Publisher: Springer ISBN: 9783642170669 Category : Business & Economics Languages : en Pages : 122
Book Description
In this book, the authors investigate structural aspects of no arbitrage pricing of contingent claims and applications of the general pricing theory in the context of incomplete markets. A quasi-closed form pricing equation in terms of artificial probabilities is derived for arbitrary payoff structures. Moreover, a comparison between continuous and discrete models is presented, highlighting the major similarities and key differences. As applications, two sources of market incompleteness are considered, namely stochastic volatility and stochastic liquidity. Firstly, the general theory discussed before is applied to the pricing of power options in a stochastic volatility model. Secondly, the issue of liquidity risk is considered by focusing on the aspect of how asset price dynamics are affected by the trading strategy of a large investor.
Author: Mr.Andreas A. Jobst Publisher: International Monetary Fund ISBN: 1475557531 Category : Business & Economics Languages : en Pages : 93
Book Description
The recent global financial crisis has forced a re-examination of risk transmission in the financial sector and how it affects financial stability. Current macroprudential policy and surveillance (MPS) efforts are aimed establishing a regulatory framework that helps mitigate the risk from systemic linkages with a view towards enhancing the resilience of the financial sector. This paper presents a forward-looking framework ("Systemic CCA") to measure systemic solvency risk based on market-implied expected losses of financial institutions with practical applications for the financial sector risk management and the system-wide capital assessment in top-down stress testing. The suggested approach uses advanced contingent claims analysis (CCA) to generate aggregate estimates of the joint default risk of multiple institutions as a conditional tail expectation using multivariate extreme value theory (EVT). In addition, the framework also helps quantify the individual contributions to systemic risk and contingent liabilities of the financial sector during times of stress.
Author: Ioannis Karatzas Publisher: ISBN: Category : Languages : en Pages : 28
Book Description
In an important and relatively recent article Bensoussan presents a rigorous treatment of the pricing problem for contingent claims that can be exercised at any time before maturity. He adapts to this situation the Black & Scholes methodology of duplicating the cash flow from such a claim by managing skillfully a self-financing portfolio that contains only the basic instruments of the market, i.e., the stocks and the bond, and that entails no arbitrage opportunities before exercise. Under a condition on the market model called completeness Bensoussan shows that the valuation of such claims is indeed possible and characterizes the exercise time in terms of an appropriate optimal stopping problem. In the study of the latter, Bensoussan employs the so-called 'penalization method, ' which forces rather stringent boundedness and regularity conditions on the payoff from the contingent claim. Such conditions are not satisfied, however, by the prototypical examples of such claims, i.e., American call options. The aim of this paper is to offer an alternative methodology on this problem, which is actually simpler and manages to remove the above restrictions.
Author: Stephen E. Satchell
Author: Stephen E. Satchell
Author: Stephen E. Satchell
Author: Sigrid Müller
Author: Tobias Herwig
Author: Bruce Neal Lehmann
Author: Angelika Esser
Author: Teemu Pennanen
Author: Bjorn Flesaker
Author: Mr.Andreas A. Jobst
Author: Ioannis Karatzas