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Abstract: Exotic interest rate derivatives are hard to value. Care must be taken to make sure that sources of volatility that impact the contingent claim are properly modeled, and that appropriate relationships are maintained between the underlying rates involved.
In this presentation, we outline the issues involved in valuing exotics. We review valuation issues for interest rate derivatives in general, and for caps, floors and swaptions. We outline a pricing methodology and apply it to Bermudan swaptions, range accruals, callable range accruals, spread options and callable spread range accruals.
Outline: - Review of interest rate modeling - Handling of vanilla options - - Forward Libor and swap rates - - Caps and Floors - - Swaptions - - Cap stripping - - Smile lifting - Bermudan valuation - - Hedging Bermudans - - LGM model specification of the HW model - - Pricing cashflows and options under the LGM model - - Model calibration - - Numerical methods - Digital options - - Pricing via vanillas. - Range accruals - - Pricing as a portfolio of digitals - - Convexity adjustment - Change of measure and approximation - Callable range accruals - - Pricing under the one factor LGM model - - - Model calibration. - - - Use of control variates (adjusters). - - Calibration and pricing under the two factor LGM model - - - Model calibration. - Spread range accruals - - Pricing under the two factor LGM model.
HJM, LGM, HW, Gaussian, linear, Markovian, Hull-White, swap, swaption, Bermudan, range, range accrual, cap, caplet, floor, digital, stripping, convexity, convexity adjustment, adjustment, adjusters, control variate, interest rate modeling, interest rate exotics
Abstract: Valuation of mortgage backed securities (MBSs) and collateralized mortgage obligations (CMOs) is the big science of the financial world. There are many moving parts, each one drawing on expertise in a different field. Prepayment modeling draws on statistical modeling of economic behavior. Data selection draws on risk analysis. Interest rate modeling draws on classic arbitrage pricing theory applied to the fixed income market. Index projection draws on statistical analysis. Making the Monte Carlo analysis tractable requires working with numerical methods and investigation of a variety of variance reduction techniques. Tractability also requires parallelization, which draws on computer science in building computation clusters and analysis and optimization of parallel algorithms. Here we detail the different components, describing the approach we have taken at Bloomberg in each area. Our particular emphasis is on the new interest rate modeling component we introduced for computing OAS, and the methods used to calibrate it accurately. We discuss the methods used to enable real time analysis of CMOs, analyzing the impact of various Monte Carlo variance reduction techniques as well as the technology used for parallelization of the computations. We also detail the validation of these components, showing that everything works well together, and yields good MBS and CMO valuation.
MBS, CMO, OAS, interest rate modeling, rate, yield, yield curve, Gaussian, Monte Carlo, parallelization, Markovian, mortgage, mortgage backed, collateralized mortgage obligation, collateralized, structured product, prepayment, prepayment modeling
Abstract: Lecture notes for a short course on FX option valuation. Includes: - Mathematical framework for FX valuation - Handling the smile and term structure for vanilla options (calls and puts): --- Interpolation issues and techniques --- Handling business time --- Handling market conventions - Pricing of barrier options: --- Attention to the joints along with the marginals --- Barrier option pricing models ------ Black-Scholes ------ Vanna-volga ------ Semi-static hedging ------ Stochastic volatility - the Heston model ------ Local volatility ------ Stochastic local volatility ------ Random risk reversal model - Hedging performance as a measure of model quality.
Foreign exchange, Forex, FX, Foreign, Call, Put, Vanilla, Black-Scholes, Vanna-volga, Hedging, Stochastic, volatility, local volatility, Random risk reversal, Stochastic skew, skew, term structure, numerical methods, interpolation, business time
Abstract: The most widely used option pricing model is the Black-Scholes model. We motivate an alternative option pricing model called the Variance Gamma (VG) model and demonstrate its implementation in the Bloomberg system.
Black-Scholes, variance gamma model, skew, kurtosis, volatility smile, option pricing, equity options, time changed Brownian motion
Abstract: Tutorial on valuation of mortgage backed securities and collateralized mortgage obligations, including: - Structure of the mortgage market - Prepayment modeling - OAS analysis - Interest rate modeling - Numerical methods - Parallelization
Abstract: The financial crisis of 2008 has highlighted the importance of assessing counterparty credit risk. Counterparty credit risk can be quantified by the credit valuation adjustment (CVA). The CVA for a bond and other securities that are long only can be calculated by using curve shifts. However, for securities that combine long and short positions (such as interest rate swaps), discount curve shifts are of limited utility. In this case, calculations must be done taking volatility into account, and essentially consist of combining appropriately adjusted swaption prices with default rates (as can be derived from CDS spreads). We have outlined the details of these calculations, and the appropriate way to compute the CVA for a swap.
CVA, risk, counterparty risk, credit risk, counterparty risk valuation, interest rate derivatives, CDS, credit default swaps, CCDS, contingent credit default swaps, interest rate swaps
Abstract: We review and detail the causes of errors in numerical differentiation, including roundoff error, convexity error, cancellation error and correlated errors. We discuss methods for improving accuracy, including step size selection and smoothing techniques, as well as a number of approaches specific to the types of computations being done.
greeks, delta, gamma, theta, differentiation, numerical, numerical differentiation, error, error control, roundoff, convexity, cancellation, smoothing, Hermite, filtering, convolution, Fourier, Gaussian, quadrature, Complex
Abstract: Interest-rate structured products and over-the-counter derivatives are like an immense, dense jungle that's grown from a small bare patch of earth in 30 years. From virtually nothing in the late 1970s, the notional value of interest-rate contracts reached $458 trillion - about eight times the gross domestic product of the world - as of June 2008, according to the Bank for International Settlements.
Here we detail tools and methodologies used for analyzing interest-rate structured products.
Structured note, interest rate derivatives, credit risk, exotic interest rate derivatives, derivatives, valuation
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