Risky Swaps

In [10] we presented a reduced form of risky bond pricing. At default date, a bond seller fails to continue fulfilling his obligation and the price of the bond sharply drops. For nodefault scenarios, if the face value of the defaulted bond is $1 then the bond price just after the default is its’ recovery rate (RR). Rating agencies and theoretical models are trying to predict RR for companies or sovereign countries. The main theoretical problem with a risky bond or with the general debt problems is presenting the price, knowing the RR. The problem of a credit default swap (CDS) pricing is somewhat an adjacent problem. Recall that the corporate bond price inversely depends on interest rate. In case of a default, the credit risk on a debt investment is related to the loss. There is a possibility for a risky bond buyer to reduce his credit risk. This can be achieved through buying a protection from a protection seller. The bondholder would pay a fixed premium up to maturity or default, which ever one comes first. If default comes before maturity, the protection buyer will receive the difference between the initial face value of the bond and RR. This difference is called ‘loss given default’. This contract represents CDS. The counterparty that pays a fixed premium is called CDS buyer or protection buyer; the opposite party is the CDS seller. Note, that in contrast to corporate bond, CDS contract does not assume that the buyer of the CDS is the holder of underlying bond. Also note that underlying to the swap can be any asset. It is called a reference asset or a reference entity. Thus, CDS is a credit instrument that separates credit risk from corresponding underlying entity. The formal type of the CDS can be described as follows. The buyer of the credit swap pays fixed rate or coupon until maturity or default in case it occurs before the maturity. If default does occur, protection buyer delivers cash or a default asset in exchange with the face value of the defaulted debt. These are known as cash or physical settlements

Risky Swaps

In [10] we presented a reduced form of risky bond pricing. At the default date a bond seller fail to continue fulfill his obligation and the price of the bond sharply drops down. If the face value of the defaulted bond for no-default scenarios is $1 then the bond price just after default is called its recovery rate (RR). Rating agencies and theoretical models are trying to predict RR for companies or sovereign countries. The main theoretical problem with a risky bond or with general debt problems is presenting the price given the RR. The problem of a credit default swap (CDS) pricing is somewhat an adjacent problem. Recall that the corporate bond price is inversely depends on interest rate. The credit risk on a debt investment is related to the loss if default occurs. There exist a possibility for a risky bond buyer to reduce his credit risk. This can be achieved by buying a protection from a protection seller. The bondholder would pay a fixed premium up to maturity or default, which one comes first. In exchange if default comes before maturity the protection buyer will receive the difference between the initially set face value of the bond and RR. This difference is called ‘loss given default’. This contract represents CDS. The counterparty that pays a fixed premium is called CDS buyer or protection buyer and the opposite party is the CDS seller. Note that in contrast to corporate bond CDS contract does not assume that buyer of the CDS is a holder of the underlying bond. Note that underlying to the swap can be any asset. It is called the reference asset or reference entity. Thus CDS is a credit instrument that separates credit risk from corresponding underlying entity. Thus the formal type of the CDS can be described as follows. The buyer of the credit swap pays fixed rate or coupon until maturity or default if it occurs sooner than maturity. In case of default protection buyer delivers cash or default asset in exchange of the face value of the defaulted debt. These are known as cash or physical settlements correspondingly.Black Scholes equation, option price, credit default swap, constant maturity default swap, equity default swap, asset swap, total return swap, credit-linked note, floating rate risky bond, counterparty risk, risky present value,

Some critical comments on credit risk modeling.

In this notice we are comment popular approaches to the credit risk modeling.Credit risk; credit derivatives; risk neutral world; risk neutral probability; structural model; reduced form

Corporate debt pricing I.

In this article we discuss fundamentals of the debt securities pricing. We begin with a generalization of the present value concept. Though the present value is the base valuation method in the modern finance we will illustrate that this concept does not sufficiently accurate in producing instrument pricing. The incompleteness of the unique present value approach stems from variability of the interest rates. Admitting variability of the interest rates we define two present values one for buyer other for seller. Therefore future buyer and seller cash payments can be described by the correspondent present values. Usually used assumption that future interest on investment over a specified time period would be the same as before specified period is a theoretical simplification that might be admitted or not. Admitting such assumption leads to eliminating an important component of the market risk. Recall that the assumption that a future payment can be invested with the same constant interest rate equal to the one used in the past is a component of the group conditions that specify frictionless of the market. We use this new concept that splits present value within two counterparties to outline details of the new valuation method of the fixed income securities. The primary goal of this paper is a credit derivative pricing method of the risky debt instruments. First we introduce a formal definition of the default. It somewhat close but does not coincide with the reduced form of the default setting.default; risky bond; reduced form model; credit risk;

Fixed-income instrument pricing.

In this article we discuss the fundamentals of pricing of the popular financial instruments. The basic point of our approach is to extend the present value benchmark concept. The present value valuation approach plays the similar role as The Newton Laws in the Classic Mechanics. Thus our primary goal is to present a new outlook on valuation of the debt securities and its derivatives. We also, demonstrate why the present value is not a complete method of pricing either securities or derivatives. Then, as illustration we present a valuation of the floating rate, callable and convertible bonds. Next we discuss major drawbacks of the risk neutral interpretation of the derivatives pricing. At the end of the article we discuss interest rate swap and derivative valuation of some classes of the fixed income securities.Bond; coupon bond; present value; floating rate bond; convertible; callable bond; interest rate swap; options valuation; risk neutral probabilities; interest rate derivatives

Multiple risky securities valuation II.

In this paper we present valuation of CDO tranches paying primary attention to the equity tranche. Our approach is close to one that was outlined in [1].CDO, tranche pricing

Multiple risky securities valuation I.

In this paper we develop an approach to valuation of a multiple names security portfolio. The goal of the paper to present pricing and calculation of the risk characteristics of the corporate debt based on randomization of the historical data of portfolio assets. Our approach close but it does not coincide with the reduced form interpretation of the credit risk. Based on stochastic interpretation of the default it follows that the market price of a bond is a stochastic process. Therefore, a spot price of a corporate bond implies risk and the bond value shows how market weights the risk. We will show in details how default correlation within securities will affect the basket exposure.Credit derivatives, risky portfolio valuation, copula, perfect copula, CDS, CDO

Risky Swaps.

In [10] we presented a reduced form of risky bond pricing. At the default date a bond seller fail to continue fulfill his obligation and the price of the bond sharply drops down. If the face value of the defaulted bond for no-default scenarios is $1 then the bond price just after default is called its recovery rate (RR). Rating agencies and theoretical models are trying to predict RR for companies or sovereign countries. The main theoretical problem with a risky bond or with general debt problems is presenting the price given the RR. The problem of a credit default swap (CDS) pricing is somewhat an adjacent problem. Recall that the corporate bond price is inversely depends on interest rate. The credit risk on a debt investment is related to the loss if default occurs. There exist a possibility for a risky bond buyer to reduce his credit risk. This can be achieved by buying a protection from a protection seller. The bondholder would pay a fixed premium up to maturity or default, which one comes first. In exchange if default comes before maturity the protection buyer will receive the difference between the initially set face value of the bond and RR. This difference is called ‘loss given default’. This contract represents CDS. The counterparty that pays a fixed premium is called CDS buyer or protection buyer and the opposite party is the CDS seller. Note that in contrast to corporate bond CDS contract does not assume that buyer of the CDS is a holder of the underlying bond. Note that underlying to the swap can be any asset. It is called the reference asset or reference entity. Thus CDS is a credit instrument that separates credit risk from corresponding underlying entity. Thus the formal type of the CDS can be described as follows. The buyer of the credit swap pays fixed rate or coupon until maturity or default if it occurs sooner than maturity. In case of default protection buyer delivers cash or default asset in exchange of the face value of the defaulted debt. These are known as cash or physical settlements correspondingly.Default, risk neutral valuation, credit default swap, constant maturity default swap, equity default swap, asset swap, total return swap, credit linked note, floating rate risky bond, counter party risk, credit spread

Risky Swaps

In [10] we presented a reduced form of risky bond pricing. At default date, a bond seller fails to continue fulfilling his obligation and the price of the bond sharply drops. For nodefault scenarios, if the face value of the defaulted bond is $1 then the bond price just after the default is its’ recovery rate (RR). Rating agencies and theoretical models are trying to predict RR for companies or sovereign countries. The main theoretical problem with a risky bond or with the general debt problems is presenting the price, knowing the RR. The problem of a credit default swap (CDS) pricing is somewhat an adjacent problem. Recall that the corporate bond price inversely depends on interest rate. In case of a default, the credit risk on a debt investment is related to the loss. There is a possibility for a risky bond buyer to reduce his credit risk. This can be achieved through buying a protection from a protection seller. The bondholder would pay a fixed premium up to maturity or default, which ever one comes first. If default comes before maturity, the protection buyer will receive the difference between the initial face value of the bond and RR. This difference is called ‘loss given default’. This contract represents CDS. The counterparty that pays a fixed premium is called CDS buyer or protection buyer; the opposite party is the CDS seller. Note, that in contrast to corporate bond, CDS contract does not assume that the buyer of the CDS is the holder of underlying bond. Also note that underlying to the swap can be any asset. It is called a reference asset or a reference entity. Thus, CDS is a credit instrument that separates credit risk from corresponding underlying entity. The formal type of the CDS can be described as follows. The buyer of the credit swap pays fixed rate or coupon until maturity or default in case it occurs before the maturity. If default does occur, protection buyer delivers cash or a default asset in exchange with the face value of the defaulted debt. These are known as cash or physical settlements.Derivatives; credit derivatives; credit default swap; total return swap; credit linked note; constant maturity default swap; equity default swap; asset swap

On stochasticity in nearly-elastic systems

Nearly-elastic model systems with one or two degrees of freedom are considered: the system is undergoing a small loss of energy in each collision with the "wall". We show that instabilities in this purely deterministic system lead to stochasticity of its long-time behavior. Various ways to give a rigorous meaning to the last statement are considered. All of them, if applicable, lead to the same stochasticity which is described explicitly. So that the stochasticity of the long-time behavior is an intrinsic property of the deterministic systems.Comment: 35 pages, 12 figures, already online at Stochastics and Dynamic