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# Simulation, Pricing, Delta Hedging & Greeks Master Package

#### About the course

A great value saving combination for practitioners and students. Includes every file from our package guides on Monte Carlo Simulation, Option Pricing, Delta Hedging, Interest Rate Simulations & IRS Pricing.

The master package includes 19 EXCEL templates and 8 handy PDF files.

A great deal for customers who wanted to buy the old subscription package that has now been discontinued.

Here are the details of the individual packages that have combined within this master package. If you need a component that is not here under the same special pricing, please let us know and we would be happy to creat a custom offer for you.

**Monte Carlo Simulation with Option pricing**

1. Derivative Pricing

This course focuses on an alternative method of implementing a two-dimensional binomial tree compared to the traditional method of building a binomial tree in excel presented in most option pricing text books.The alternate approach is based on the techniques documented by Professor Mark Broadie at Columbia Business School as part of his coursework in Security Pricing and Computational Finance courses at Columbia University and allows us to extend a simple 3 step tree to a 50 – 100 step option pricing tree in a few minutes. It uses this alternative approach to price European & American calls and put options and Knock out and Knock in (Sudden Death) options.

2. Monte Carlo Simulation – Models and Applications

The "Monte Carlo Simulation – Models and Applications" study guide includes topics on how to build Monte Carlo simulators in EXCEL and use these models to price vanilla and exotic options; how to calculate VaR for futures and options; an alternative approach to the original Monte Carlo simulator using historical returns rather than normally distribution returns and the impact of this approach on VaR numbers; fuel hedging risk management case studies; further applications like simulating interest rate term structures and forecasting the monetary policy rate.

The Monte Carlo Simulation with Option pricing package guide also includes the following EXCEL files:

- The supporting excel file for the alternate binomial tree methodology for the products mentioned above
- Option pricing using the Traditional Binomial Tree approach
- Option pricing using the Black-Scholes option pricing formula
- An example of how the Ladder call option may be priced using Monte Carlo Simulation in EXCEL (standalone Excel file)
- Derivative Pricing using Monte Carlo Simulation EXCEL file calculates the option prices for a number of vanilla and exotic options including Asian, Barrier, Lookback & Chooser Options.

**Interest Rate Simulation**

The PDF file covers:

- Components of interest rate models
- Features of good models
- Criteria employed when selecting models
- Differences between various types of term structure models
- Estimation and calibration of parameters for, and construction of, the one-factor equilibrium Cox-Ingersoll-Ross (CIR) model
- Construction and utilization of the one-factor no-arbitrage Black-Derman-Toy (BDT) model
- Principal Component Analysis (PCA) for the determination of a workable number of components / factors for the Heath, Jarrow, Merton (HJM) model
- Construction of the multi-factor no-arbitrage Heath-Jarrow-Merton (HJM) model

EXCEL files included:

- Zero Coupon and Forward rate term structures derivation and construction (pre-requisite)
- Calibration of a CIR Model's parameters to a historical rates data set
- Construction of a BDT model
- Utilization of the results of a BDT model
- Principal Component Analysis
- Construction of a HJM 3-factor model

**Hedging Higher Order Greek**

The course provides a step by step guide on how to build a hedging model that considers hedging the higher order Greeks of the trader’s position. The model is EXCEL based and uses the Solver functionality. The course discusses the setting and purpose of the objective function and constraints. It explains the results in light of various objectives including lower cost, minimization of gamma & vega, etc.

Two simplistic illustrations, one based on hedging a single short position, the other based on hedging a portfolio of short positions, walk the reader through the various elements of the model. Tweaks to the base model are discussed to show how results are impacted when constraints and objectives are changed. Constraint redundancy and portfolio allocation limits are also considered.

The package consists of a PDF course and supporting EXCEL file containing the model.

**Constructing Volatility Surfaces in EXCEL**

A volatility surface plots market consistent volatilities across moneyness (strike prices) and maturity (time to expiry). Within the surface market consistent volatilities are referred to as local volatilities. Rather than backing out volatility by applying the Black Scholes model in reverse to at the money options, local volatilities use implied volatilities and a one factor Black Scholes model to drive local volatility values across the surface.

Volatility surfaces, like Option Greeks, are among the last topics that get covered in a graduate level course on option pricing. Most schools and professors give it a wide berth in undergraduate and graduate level courses since it is based on an advance practitioner level understanding of the subject. While the topic may get some coverage in a level I course, a level II or level III course is what you need to enroll into to finally build the surface.

If you are familiar with Black Scholes equation and pricing models used for pricing European options, calibrating volatility surfaces is one of the tweaks market practitioners use to side step the constant volatility assumption.

The volatility surface package includes the following:

- A 30 page PDF guide that shows how to build a volatility surface step by step in EXCEL using Dupire's formula.
- An EXCEL spreadsheet that is used as a simple teaching template by the PDF tutorial above. The Excel sheet shows the implementation of Dupire's formula as well as the resultant volatility surface. The sheet also shows Taleb's implementation of implied forward volatility using term structure of volatility concepts.

**Delta Hedging Greeks - EXCEL**

This product contains 3 EXCEL files.

1. Greeks

- Calculation of the Black Scholes option price for a European Call and a European Put option
- Calculation of Greeks- Delta, Gamma, Vega, Theta & Rho- for a European Call and a European Put option
- Data table that captures the Black Scholes risk adjusted probabilities and option premium across a series of volatilities
- Graphical representation of Black Scholes risk adjusted probabilities and option premium against volatilities
- Data tables that capture the sensitivity of the Greeks against Spot, Strike, Time to maturity, Volatility and the Risk Free Rate respectively
- Graphical representation of the sensitivities of the various Greeks against Spot, Strike, Time to maturity, volatility and risk free rate respectively

2. Delta Hedging – Call Option

- Calculation of a 12-step Monte Carlo simulation model that generates the underlying stock price series
- Calculation of theoretical option values using the Black Scholes call option price formula
- Calculation of call option deltas at each rebalancing interval
- Calculation of a replicating portfolio that consists of a long position in Delta times the stock and a short position in the amount borrowed (net of the option premium received at inception) to fund the initial & subsequent incremental purchases
- Graphical representation of the theoretical option value and the replicating portfolio value over the life of the option
- Calculation of a tracking error for the difference between the value of the replicating portfolio and the theoretical value of the option
- Graphical representation of the tracking error across the life of the option
- Determination of the per period interest and principal portions of the amount borrowed
- Determination of the Gain (Loss) on sale of portions of the stock
- Setting up a Cash Accounting P&L that shows cash inflows from option premium received and strike received in the event the option is exercise and cash outflows from interest and principal repayment on the amount borrowed
- A choice of including of excluding the option premium in determining the amount borrowed at inception. In this case the Principal repaid will equal the gain (loss) if the option is not exercised.
- 100 simulated runs including a graphical depiction of the results showing the Net P&L, Amount borrowed (principal & interest) and Gain/ Losses; and averages across the 100 runs for each of these items

3. Delta Hedging – Put Option

- Calculation of a 12-step Monte Carlo simulation model that generates the underlying stock price series
- Calculation of theoretical option values using the Black Scholes put option price formula
- Calculation of put option deltas at each rebalancing interval
- Calculation of a replicating portfolio that consists of a short sale of Delta times the stock and lending of the initial (net of the option premium received at inception) & subsequent incremental short sales proceeds
- Graphical representation of the theoretical option value and the replicating portfolio value over the life of the option
- Calculation of a tracking error for the difference between the value of the replicating portfolio and the theoretical value of the option
- Graphical representation of the tracking error across the life of the option
- Determination of the per period interest and principal portions of the amount lent
- Determination of the Gain (Loss) on closing of short sale positions
- Setting up a Cash Accounting P&L that shows cash inflows from option premium received, interest earned on amount lent and sales proceeds from short sales and cash outflows from strike paid if the option is exercised
- A choice of including or excluding the option premium in determining the amount borrowed at inception. In this case the sales proceeds from short sales will equal the gain (loss) if the option is not exercised.
- 100 simulated runs including a graphical depiction of the results showing the Net P&L, Proceeds from Short Sales, Interest Earned and Gain/ Losses; and averages across the 100 runs for each of these items

**Pricing Interest Rate Swaps & Options**

Topics covered:

- Definition of different types of interest rates
- Overview of swap contract variations
- Summary of the pricing process for interest rate swaps
- Step-by-step methodology for deriving zero coupon and forward rate term structures
- Step-by-step procedures for determining the price of interest rate swaps, Cross currency swaps,Interest rate options

The EXCEL files:

- The calculation of zero coupon and forward rate curves from the par term structure
- The calculation of prices of interest rate swaps and cross currency swaps
- The calculation of prices of interest rate options

#### Learning Objectives

After taking this course you will be able to:

- Understand and appreciate the calculation efficiency of the alternate binomial trees approach
- Calculate the price of various options using this approach including European call & put options, American call & put options, capped calls with automatic exercise, knock in and knock out options
- Price European and American call and put options using the traditional binomial tree approach
- Price European call, put and various barrier options using the Black Scholes formula
- Calculate the Greeks for these options using the Black Scholes formula & binomial trees
- Construct a basic Monte Carlo simulator in EXCEL to determine possible future price paths for equities, commodities or currencies
- Build a hybrid Monte Carlo simulation model that uses the actual historical return distribution instead of the normal distribution assumption used in the original version
- Explain and analyze Black Scholes risk adjusted probabilities using a Monte Carlo simulation model
- Price vanilla and exotic options using a Monte Carlo simulation model
- Apply convergence and variance reduction techniques to improve the accuracy of Monte Carlo simulation results
- Calculate Value at Risk (VaR) for futures and options using the Monte Carlo simulation approach
- Calculate Value at Risk using the Monte Carlo simulation model that makes use of the actual historical return distribution and compare the result to results from the original Monte Carlo simulation and Historical Simulation VaR approaches
- Analyze the effectiveness of entering a hedging program for the aviation industry using Monte Carlo simulation
- Simulate the term structure of interest rates using the Cox-Ingersoll Ross (CIR) interest rate model & the Heath-Jarrow-Merton (HJM) multifactor interest rate model
- Forecast the monetary policy rate using a simplified Monte Carlo simulation model
- List the features of a good model
- Distinguish between equilibrium and no arbitrage models
- Describe one factor and multifactor models
- Describe the different types of interest rates
- Bootstrap zero and forward term structures from par term structures
- Explain why this the MC simulator using for determining the price/ rate of commodities, stock and currencies cannot be extended to interest rates
- Use discrete interest rate data with simple or covariance equivalent discretisation representation to estimate the parameters of the continuous CIR model
- Apply the least squares method to calibrate the model to a given historical interest rates data set
- Simulate the future short term rates from the CIR model process and the estimated parameters
- Derive longer term rates from the simulated short term rates and the perfect correlation assumption of the one factor model
- Describe the basic features of the BDT interest rate model
- List the simplifying assumptions used in the construction of the model
- Build a BDT model in EXCEL
- Derive results for the model, i.e. the median rates and time varying volatilities by setting and running the Solver functionality in EXCEL
- Build the short rates tree from the outputs of the BDT model (median rates, volatilities and calculated up-movements)
- Calculate the price of fixed income bonds using the derived short rate tree
- Calculate the price of options using the derived short rate
- Compute the principal components (eigenvectors) and their relative importance factors (eigenvalues) for the underlying term structure using EXCEL’s matrix multiplication, inverse matrix & Solver functionalities
- Determine functions for the selected eigenvectors/ principal components
- Calculate the scaling factor for each component function’s so that the combined volatilities derived from these functions match the volatilities inherent in the underlying term structure
- Calculate Brownian shocks
- Calculate the principal component factor based drifts
- Construct the HJM interest rate model comprising of a spot and forwards rates tree
- Calculate the discount factor or one-period price tree from the HJM interest rate model
- Calculate the value of a bond using the price tree derived above
- Calculate Greeks - Delta, Gamma, Vega, Rho & Theta - for an option portfolio as a whole, for both the short position portfolio and the hedge portfolio
- Build a Solver based model in EXCEL to hedge against higher order Greeks in the short position portfolio
- Change model parameters to satisfy certain criteria and objectives, fine tune results, and assess constraint redundancy/ usefulness
- Assess and interpret results, recommended allocations and cost
- Graph Black Scholes risk adjusted probabilities and option premium against varying volatilities
- Calculate and graph the sensitivity of Greeks to changing Spot, Strike, Time to maturity, Volatility and the Risk Free Rate respectively
- Build a delta hedging model for European call and put options
- Create replicating portfolios for European call and put options
- Calculate tracking errors between replicating portfolio and theoretical option values
- Set up a Cash Accounting P&L for the option and the hedging portfolio
- Present the results of the simulation runs for Net P&L, Amount borrowed/Proceeds from Short sales, Gains and Losses, etc
- Distinguish between trailing, implied and local volatilities
- Calculate implied volatility
- Calculate local volatility using Dupire’s formula
- Understand the advantages of purchasing a deep out of the money option
- Construct a volatility surface of implied volatilities in EXCEL
- Construct a volatility surface of local volatilities in EXCEL
- Calculate a term structure of forward implied volatilities in EXCEL
- Define cash flows
- Understand why cash flows need to be discounted
- Understand how spot, forward and short rates are linked
- Define yield to maturity
- Understand what a term structure of interest rates is
- Define forward rate agreements and forward contracts
- List and define the various types of swaps
- Outline a process for pricing interest rate swaps
- Define & price coupon swaps
- Define & price basis swaps
- Define & price fixed for fixed cross currency swaps
- Define & price floating for floating cross currency swaps
- Define & price amortizing floating for floating currency swaps
- Define and price caps and floors
- Understand how the cap floor parity may be used to price a swap
- Define and price accrual swaps
- Define and price commodity linked notes
- Define and price range accrual note

#### Prerequisites

Familiarity with EXCEL including the Solver functionality & the VLOOKUP, HLOOKUP NORMSDIST & STDEV functions, mathematics, statistics, probability and regression/ curve fitting analysis. Some knowledge of bond and derivative markets.

#### Target Audience

The course is aimed at professionals who deal with pricing, valuation and risk issues related to money market, derivatives, structured products and foreign exchange transactions, as well as individuals responsible for capital allocation, limit setting, stress testing, asset liability management and risk management within banks, insurance companies, mutual funds, as well as finance departments of non-financial organizations.