1,176 research outputs found
A Common Market Measure for Libor and Pricing Caps, Floors and Swaps in a Field Theory of Forward Interest Rates
The main result of this paper that a martingale evolution can be chosen for
Libor such that all the Libor interest rates have a common market measure; the
drift is fixed such that each Libor has the martingale property. Libor is
described using a field theory model, and a common measure is seen to be emerge
naturally for such models. To elaborate how the martingale for the Libor
belongs to the general class of numeraire for the forward interest rates, two
other numeraire's are considered, namely the money market measure that makes
the evolution of the zero coupon bonds a martingale, and the forward measure
for which the forward bond price is a martingale. The price of an interest rate
cap is computed for all three numeraires, and is shown to be numeraire
invariant. Put-call parity is discussed in some detail and shown to emerge due
to some non-trivial properties of the numeraires. Some properties of swaps, and
their relation to caps and floors, are briefly discussed.Comment: 28 pages, 4 figure
Exploring mispricing in the term structure of CDS spreads
YesBased on a reduced-form model of credit risk, we explore mispricing in the CDS spreads of North
American companies and its economic content. Specifically, we develop a trading strategy using the
model to trade out of sample market-neutral portfolios across the term structure of CDS contracts. Our
empirical results show that the trading strategy exhibits abnormally large returns, confirming the existence
and persistence of a mispricing. The aggregate returns of the trading strategy are positively related
to the square of market-wide credit and liquidity risks, indicating that the mispricing is more pronounced
when the market is more volatile. When implemented on the Markit data, the strategy shows significant
economic value even after controlling for realistic transaction costs
Pricing Options On Risky Assets In A Stochastic Interest Rate Economy 1
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73150/1/j.1467-9965.1992.tb00030.x.pd
Derivatives and Credit Contagion in Interconnected Networks
The importance of adequately modeling credit risk has once again been
highlighted in the recent financial crisis. Defaults tend to cluster around
times of economic stress due to poor macro-economic conditions, {\em but also}
by directly triggering each other through contagion. Although credit default
swaps have radically altered the dynamics of contagion for more than a decade,
models quantifying their impact on systemic risk are still missing. Here, we
examine contagion through credit default swaps in a stylized economic network
of corporates and financial institutions. We analyse such a system using a
stochastic setting, which allows us to exploit limit theorems to exactly solve
the contagion dynamics for the entire system. Our analysis shows that, by
creating additional contagion channels, CDS can actually lead to greater
instability of the entire network in times of economic stress. This is
particularly pronounced when CDS are used by banks to expand their loan books
(arguing that CDS would offload the additional risks from their balance
sheets). Thus, even with complete hedging through CDS, a significant loan book
expansion can lead to considerably enhanced probabilities for the occurrence of
very large losses and very high default rates in the system. Our approach adds
a new dimension to research on credit contagion, and could feed into a rational
underpinning of an improved regulatory framework for credit derivatives.Comment: 26 pages, 7 multi-part figure
Multivariate risks and depth-trimmed regions
We describe a general framework for measuring risks, where the risk measure
takes values in an abstract cone. It is shown that this approach naturally
includes the classical risk measures and set-valued risk measures and yields a
natural definition of vector-valued risk measures. Several main constructions
of risk measures are described in this abstract axiomatic framework.
It is shown that the concept of depth-trimmed (or central) regions from the
multivariate statistics is closely related to the definition of risk measures.
In particular, the halfspace trimming corresponds to the Value-at-Risk, while
the zonoid trimming yields the expected shortfall. In the abstract framework,
it is shown how to establish a both-ways correspondence between risk measures
and depth-trimmed regions. It is also demonstrated how the lattice structure of
the space of risk values influences this relationship.Comment: 26 pages. Substantially revised version with a number of new results
adde
Local time and the pricing of time-dependent barrier options
A time-dependent double-barrier option is a derivative security that delivers
the terminal value at expiry if neither of the continuous
time-dependent barriers b_\pm:[0,T]\to \RR_+ have been hit during the time
interval . Using a probabilistic approach we obtain a decomposition of
the barrier option price into the corresponding European option price minus the
barrier premium for a wide class of payoff functions , barrier functions
and linear diffusions . We show that the barrier
premium can be expressed as a sum of integrals along the barriers of
the option's deltas \Delta_\pm:[0,T]\to\RR at the barriers and that the pair
of functions solves a system of Volterra integral
equations of the first kind. We find a semi-analytic solution for this system
in the case of constant double barriers and briefly discus a numerical
algorithm for the time-dependent case.Comment: 32 pages, to appear in Finance and Stochastic
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