共查询到20条相似文献,搜索用时 31 毫秒
1.
Dynamic programming and mean-variance hedging 总被引:4,自引:0,他引:4
2.
3.
4.
Sven Rady 《Finance and Stochastics》1997,1(4):331-344
This paper uses a probabilistic change-of-numeraire technique to compute closed-form prices of European options to exchange
one asset against another when the relative price of the underlying assets follows a diffusion process with natural boundaries
and a quadratic diffusion coefficient. The paper shows in particular how to interpret the option price formula in terms of
exercise probabilities which are calculated under the martingale measures associated with two specific numeraire portfolios.
An application to the pricing of bond options and certain interest rate derivatives illustrates the main results. 相似文献
5.
LIBOR and swap market models and measures 总被引:9,自引:0,他引:9
Farshid Jamshidian 《Finance and Stochastics》1997,1(4):293-330
A self-contained theory is presented for pricing and hedging LIBOR and swap derivatives by arbitrage. Appropriate payoff
homogeneity and measurability conditions are identified which guarantee that a given payoff can be attained by a self-financing
trading strategy. LIBOR and swap derivatives satisfy this condition, implying they can be priced and hedged with a finite
number of zero-coupon bonds, even when there is no instantaneous saving bond. Notion of locally arbitrage-free price system
is introduced and equivalent criteria established. Stochastic differential equations are derived for term structures of forward
libor and swap rates, and shown to have a unique positive solution when the percentage volatility function is bounded, implying
existence of an arbitrage-free model with such volatility specification. The construction is explicit for the lognormal LIBOR
and swap “market models”, the former following Musiela and Rutkowski (1995). Primary examples of LIBOR and swap derivatives
are discussed and appropriate practical models suggested for each. 相似文献
6.
Complete markets with discontinuous security price 总被引:4,自引:0,他引:4
7.
8.
9.
10.
11.
12.
HAIM LEVY 《The Journal of Finance》1985,40(4):1197-1217
Applying stochastic dominance rules with borrowing and lending at the risk-free interest rate, we derive upper and lower values for an option price for all unconstrained utility functions and alternatively for concave utility functions. The derivation of these bounds is quite general and fits any kind of stock price distribution as long as it is characterized by a “nonnegative beta.” Transaction costs and taxes can be easily incorporated in the model presented here since investors are not required to revise their portfolios continuously. The “price” that is paid for this generalization is that a range of values rather than a unique value is obtained. 相似文献
13.
Asymptotic arbitrage in large financial markets 总被引:3,自引:0,他引:3
A large financial market is described by a sequence of standard general models of continuous trading. It turns out that the
absence of asymptotic arbitrage of the first kind is equivalent to the contiguity of sequence of objective probabilities with
respect to the sequence of upper envelopes of equivalent martingale measures, while absence of asymptotic arbitrage of the
second kind is equivalent to the contiguity of the sequence of lower envelopes of equivalent martingale measures with respect
to the sequence of objective probabilities. We express criteria of contiguity in terms of the Hellinger processes. As examples,
we study a large market with asset prices given by linear stochastic equations which may have random volatilities, the Ross
Arbitrage Pricing Model, and a discrete-time model with two assets and infinite horizon. The suggested theory can be considered
as a natural extension of Arbirage Pricing Theory covering the continuous as well as the discrete time case. 相似文献
14.
We establish the equivalence of competitive industry equilibrium with a central planner's decision problem under uncertainty,
when investment is irreversible. The existence of industry equilibrium is derived, and it is shown that myopic behavior on
the part of small agents is harmless, in the sense that it leads to the same decisions as full rational expectations do. Our
model is set in continuous time and allows for very general forms of randomness. The methods are based on the probabilistic
approach to singular stochastic control theory and its connections with optimal stopping problems. 相似文献
15.
Towards a general theory of bond markets 总被引:1,自引:0,他引:1
Tomas Björk Giovanni Di Masi Yuri Kabanov Wolfgang Runggaldier 《Finance and Stochastics》1997,1(2):141-174
The main purpose of the paper is to provide a mathematical background for the theory of bond markets similar to that available
for stock markets. We suggest two constructions of stochastic integrals with respect to processes taking values in a space
of continuous functions. Such integrals are used to define the evolution of the value of a portfolio of bonds corresponding
to a trading strategy which is a measure-valued predictable process. The existence of an equivalent martingale measure is
discussed and HJM-type conditions are derived for a jump-diffusion model. The question of market completeness is considered
as a problem of the range of a certain integral operator. We introduce a concept of approximate market completeness and show
that a market is approximately complete iff an equivalent martingale measure is unique. 相似文献
16.
17.
18.
19.
This paper studies the impact, on no-arbitrage conditions, of stopping the price process at an arbitrary random time. As price processes, we consider the class of quasi-left-continuous semimartingales, i.e., semimartingales that do not jump at predictable stopping times. We focus on the condition of no unbounded profit with bounded risk (called NUPBR), also known in the literature as no arbitrage of the first kind. The first principal result describes all the pairs of quasi-left-continuous market models and random times for which the resulting stopped model fulfils NUPBR. Furthermore, for a subclass of quasi-left-continuous local martingales, we construct explicitly martingale deflators, i.e., strictly positive local martingales whose product with the price process stopped at a random time is a local martingale. The second principal result characterises the random times that preserve NUPBR under stopping for any quasi-left-continuous model. The analysis carried out in the paper is based on new stochastic developments in the theory of progressive enlargements of filtrations. 相似文献
20.
Jean-Pierre Fouque George Papanicolaou K. Ronnie Sircar 《Asia-Pacific Financial Markets》1999,6(1):37-48
We present a derivative pricing and estimation methodology for a class of stochastic volatility models that exploits the observed
'bursty' or persistent nature of stock price volatility. Empirical analysis of high-frequency S&P 500 index data confirms
that volatility reverts slowly to its mean in comparison to the tick-by- tick fluctuations of the index value, but it is fast
mean- reverting when looked at over the time scale of a derivative contract (many months). This motivates an asymptotic analysis
of the partial differential equation satisfied by derivative prices, utilizing the distinction between these time scales.
The analysis yields pricing and implied volatility formulas, and the latter provides a simple procedure to 'fit the skew'
from European index option prices. The theory identifies the important group parameters that are needed for the derivative
pricing and hedging problem for European-style securities, namely the average volatility and the slope and intercept of the
implied volatility line, plotted as a function of the log- moneyness-to-maturity-ratio. The results considerably simplify
the estimation procedure. The remaining parameters, including the growth rate of the underlying, the correlation between asset
price and volatility shocks, the rate of mean-reversion of the volatility and the market price of volatility risk are not
needed for the asymptotic pricing formulas for European derivatives, and we derive the formula for a knock-out barrier option
as an example. The extension to American and path-dependent contingent claims is the subject of future work.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献