Tài chính doanh nghiệp - Topic 14: Selecting distributions, distribution fitting and the normal curve using @risk l. gattisDistribution fitting is the process of fitting a curve (or geometric shape) to a histogram to use in simulations The Normal distribution is the most used in finance and other fields We will now compare and use other distributions
23 trang | Chia sẻ: huyhoang44 | Ngày: 27/03/2020 | Lượt xem: 538 | Lượt tải: 0
Tài chính doanh nghiệp - Topic 13B: Bsm option greeks and dynamic delta hedgingDynamic hedging is an active hedging strategy where the delta positions are adjusted continuously (or at least daily) Since option gamma’s are nonzero, the deltas will change as the underlying stock price changes.
30 trang | Chia sẻ: huyhoang44 | Ngày: 27/03/2020 | Lượt xem: 554 | Lượt tải: 0
Tài chính doanh nghiệp - Topic 13A: Black - Scholes - merton option pricing model, implied vols, and volatility estimationEmpirical studies have found autocorrelation in volatility which means high vol is likely to be followed by high vol (“Volatility Clustering”). Sample and population volatility measures equally weight historical data when computing volatility Exponential Weighted Moving Average Volatility (EWMA) is a volatility estimate that weighs recent data mo...
25 trang | Chia sẻ: huyhoang44 | Ngày: 27/03/2020 | Lượt xem: 590 | Lượt tải: 0
Tài chính doanh nghiệp - Topic 13: Option contracts and hedging, monte carlo valuation, and black - ScholesFunction stocksim_cont(s, r, d, v, h, z) stocksim_cont = s * Exp((r - d - 0.5 * v ^ 2) * h + v * z * h ^ 0.5) End Function ---------------------------------------------------------------------------------- S: Current Stock Price; d: annualized dividend yield; z: random ~N(0,1); h: time (in years) between stock price changes; if you model stoc...
26 trang | Chia sẻ: huyhoang44 | Ngày: 27/03/2020 | Lượt xem: 513 | Lượt tải: 0
Tài chính doanh nghiệp - Topic 12: Forward contracts and hedges, simulated correlated random variables5 years of monthly jet fuel, Gas, and Heating Oil Prices. Monthly price returns and correlation matrix Compute monthly returns and correlation matrix Jet Fuel and Heating Oil have highest correlation (.97) Compute Jet Fuel / Heating Oil beta, =Slope(Jet Returns, Oil) Cross Hedging Strategy: Enter into contract to buy 93,750 gallons of heating o...
25 trang | Chia sẻ: huyhoang44 | Ngày: 27/03/2020 | Lượt xem: 497 | Lượt tải: 0
Tài chính doanh nghiệp - Topic 11B: Accrued interest, clean and dirty prices, yield curve models, and forward ratesSpot rates are interest rates on instruments that start today and mature at a future date (t). Written r(0,t) Forward rates are interest rates on instruments that start at a future date (t1) and mature at a later future date (t2). Written r(t1,t2) Forward interest rates are used to “lock into” future investment or borrowing interest rates You ...
25 trang | Chia sẻ: huyhoang44 | Ngày: 27/03/2020 | Lượt xem: 587 | Lượt tải: 0
Tài chính doanh nghiệp - Topic 11A: Default - Adjusted bond returnIn the prior examples, the formulas calculated the returns for annual payment bonds To adjust for semi-annual payments, divide the coupon rate by 2 and multiply the term by 2. You must also adjust the transition matrix to six-month periods The resulting default adjusted return will be a 6-month return. Multiply this number by 2 to report the bon...
22 trang | Chia sẻ: huyhoang44 | Ngày: 27/03/2020 | Lượt xem: 528 | Lượt tải: 0
Tài chính doanh nghiệp - Topic 11: Fixed income portfolio optimizationIn the prior slide, I replaced the durations and convexities with values to reflect the prepayment options of consumer loans Durations and negative convexity values would come from other models (not addressed in this class) that compute the duration and convexity of loans based on borrowers prepayment behaviors (prepayment models) The bond value,...
17 trang | Chia sẻ: huyhoang44 | Ngày: 27/03/2020 | Lượt xem: 474 | Lượt tải: 0
Tài chính doanh nghiệp - Topic 10: Bond valuation, ytm, duration, convexity, and bond varNegative convexity (interest rate risk) of mortgages is not attractive to investors (or banks) if rates fall or rise As rates fall non-callable bond price will appreciate according to its duration (and even more due to convexity) Mortgage do not appreciate much because the mortgage can always be prepaid at par (limited upside!) Worse yet, as ra...
28 trang | Chia sẻ: huyhoang44 | Ngày: 27/03/2020 | Lượt xem: 604 | Lượt tải: 0
Tài chính doanh nghiệp - Topic 8: Dynamic portfolio simulation, monte carlo, personal financial planning models, @riskSimulate portfolios with multiple periods, changing asset allocation, and contributions Create a personal financial planning model Use @Risk and Macros to run Monte Carlo Simulations Use @Risk Goal Seek
13 trang | Chia sẻ: huyhoang44 | Ngày: 27/03/2020 | Lượt xem: 680 | Lượt tải: 0
