eBook - ePub
Modern Derivatives Pricing and Credit Exposure Analysis
Theory and Practice of CSA and XVA Pricing, Exposure Simulation and Backtesting
Roland Lichters, Roland Stamm, Donal Gallagher
This is a test
Partager le livre
- English
- ePUB (adapté aux mobiles)
- Disponible sur iOS et Android
eBook - ePub
Modern Derivatives Pricing and Credit Exposure Analysis
Theory and Practice of CSA and XVA Pricing, Exposure Simulation and Backtesting
Roland Lichters, Roland Stamm, Donal Gallagher
DĂ©tails du livre
Aperçu du livre
Table des matiĂšres
Citations
Ă propos de ce livre
This book provides a comprehensive guide for modern derivatives pricing and credit analysis. Written to provide sound theoretical detail but practical implication, it provides readers with everything they need to know to price modern financial derivatives and analyze the credit exposure of a financial instrument in today's markets.
Foire aux questions
Comment puis-je résilier mon abonnement ?
Il vous suffit de vous rendre dans la section compte dans paramĂštres et de cliquer sur « RĂ©silier lâabonnement ». Câest aussi simple que cela ! Une fois que vous aurez rĂ©siliĂ© votre abonnement, il restera actif pour le reste de la pĂ©riode pour laquelle vous avez payĂ©. DĂ©couvrez-en plus ici.
Puis-je / comment puis-je télécharger des livres ?
Pour le moment, tous nos livres en format ePub adaptĂ©s aux mobiles peuvent ĂȘtre tĂ©lĂ©chargĂ©s via lâapplication. La plupart de nos PDF sont Ă©galement disponibles en tĂ©lĂ©chargement et les autres seront tĂ©lĂ©chargeables trĂšs prochainement. DĂ©couvrez-en plus ici.
Quelle est la différence entre les formules tarifaires ?
Les deux abonnements vous donnent un accĂšs complet Ă la bibliothĂšque et Ă toutes les fonctionnalitĂ©s de Perlego. Les seules diffĂ©rences sont les tarifs ainsi que la pĂ©riode dâabonnement : avec lâabonnement annuel, vous Ă©conomiserez environ 30 % par rapport Ă 12 mois dâabonnement mensuel.
Quâest-ce que Perlego ?
Nous sommes un service dâabonnement Ă des ouvrages universitaires en ligne, oĂč vous pouvez accĂ©der Ă toute une bibliothĂšque pour un prix infĂ©rieur Ă celui dâun seul livre par mois. Avec plus dâun million de livres sur plus de 1 000 sujets, nous avons ce quâil vous faut ! DĂ©couvrez-en plus ici.
Prenez-vous en charge la synthÚse vocale ?
Recherchez le symbole Ăcouter sur votre prochain livre pour voir si vous pouvez lâĂ©couter. Lâoutil Ăcouter lit le texte Ă haute voix pour vous, en surlignant le passage qui est en cours de lecture. Vous pouvez le mettre sur pause, lâaccĂ©lĂ©rer ou le ralentir. DĂ©couvrez-en plus ici.
Est-ce que Modern Derivatives Pricing and Credit Exposure Analysis est un PDF/ePUB en ligne ?
Oui, vous pouvez accĂ©der Ă Modern Derivatives Pricing and Credit Exposure Analysis par Roland Lichters, Roland Stamm, Donal Gallagher en format PDF et/ou ePUB ainsi quâĂ dâautres livres populaires dans Volkswirtschaftslehre et Ăkonometrie. Nous disposons de plus dâun million dâouvrages Ă dĂ©couvrir dans notre catalogue.
Informations
Sous-sujet
ĂkonometrieI
Discounting
1 | Discounting Before the Crisis |
1.1 The risk-free rate
The main ingredient for pricing is the zero curve r(t) which assigns an interest rate to any given maturity t > 0. It tells us what the value of 1 currency unit will be at time t if invested at the risk-free rate. For most theoretical applications, the zero rate is expressed as continuously compounding, so the value at time t will be given by
Other conventions are also common. Linear compounding is typically used for short-term interest (less than one year):
Simple compounding takes interest on interest into account, in particular for maturities beyond one year:
Conversely, todayâs value of one currency unit paid in t years is given by
P(0,t) is the price of a risk-free zero bond with maturity t, as seen today (at time 0). It is also referred to as the (deterministic) discount factor for time t, dft.
This immediately raises the question: What is the risk-free rate, which is the compensation to lenders for not using their money for consumption immediately? The person or institution making the promise of paying back the money would have to be seen as non-defaultable, no matter what happens. Obviously, such an entity does not exist, so people use proxies like certain highly rated governments or supra-national institutions. Before the near-default of Bear Stearns, people viewed banks that were rated AA or higher as virtually default-free, and therefore used the LIBOR rate as proxies for the risk-free rate.
1.2 Pricing linear instruments
1.2.1 Forward rate agreements
The most important building block in interest rate modelling is the forward rate agreement, or FRA for short. This is a contract by which two parties agree today (at t = 0) on an interest rate f(0;t1,t2) to be paid in t2 for a loan spanning a future period t1 to t2. If the market (i.e. LIBOR) rate L(t1,t2) which is fixed in t1 for that period exceeds f(0;t1,t2), the payer of the rate has made a profit. Otherwise, the receiver gains more than the market rate.
Market practice is that the payment is actually paid in t1 by computing the cash flow in t2 and discounting it to t1 with the fixed LIBOR rate. For pricing purposes, this is virtually irrelevant (see [117]), so we ignore this distinction.
Pricing this correctly is obviously equivalent to predicting the LIBOR rate in a market-accepted manner.
What rate can we expect in three monthsâ time if we want to borrow money for six months at that time? Calculate the forward rate of a 3M into 9M FRA as follows:
âą Borrow df0.25 = P(0,0.25) units for three months at the risk-free three-month rate
âą Invest the money for nine months at the risk-free rate for nine months
âą Borrow 1 unit in an FRA in three months (maturing six months later) to pay back the loan with interest
âą After another six months, pay back the loan with the df0.25/df0.75 from the investment
âą By the no-arbitrage principle, the combination has to be worth 0. The forward rate therefore has to be
Note that, in general, the period lengths are not exactly a quarter or half a year but rather depend on the day count fraction of the rates used. In Euroland, this would be ACT/360, for example.
In Figure 1.1, we must have (assuming linear compounding, as is the market custom for periods of less than one year)
In other words
In general, the forward rate for time t (in years from today) for a period of ÎŽ (in years) is given by
The present value of the forward rate paid on a notional of 1 unit is therefore
Note that this is true because we use the same discount factors in the forward rate replication as when discounting cash flows. The main assumption in this replication argument is that I (at least a bank) can borrow and lend arbitrary amounts at the risk-free (LIBOR) rate.
We can take a look at what happens if we let ÎŽ approach 0 in formula (1.1), under the assumption that the discount curve is differentiable:
which also implies that
Forward rates are used as expected values for the LIBOR fixing for a future time period. Most importantly, this is done in interest rate swaps.
1.2.2 Interest rate swaps
An interest rate swap, or swap for short, is a contract by which two parties agree to exchange interest payments on a predetermined notional on a regular basis. One party pays the fixed rate with the frequency which is standard in the chosen currency. For EUR, for instance, this is annually; for USD, on the other hand, this is semi-annually. The other party pays a floating rate linked to LIBOR of some given frequency (1, 3, 6 or 12 months), possibly with a spread. There is also a standard frequency for floating legs in most currencies: in EUR, this is six months, and in USD, it is three months, for instance.
At inception, the v...