A project on energy derivatives. We needto examine revenue puts: a currently popularhedge for project nance of generation. The following is a substantiallysimplified version in practice both the asset and the revenue put involvesimulation and exercise mechanics at the hourly time-scale, often at highly

illiquid delivery locations.

TradeDate PJM Dec16 ADHUB Dec16 4/8/2015 42.4 37.75 4/9/2015 42.1 37.65 4/10/2015 41.95 37.9 4/13/2015 42.3 38.05 4/14/2015 42.35 38 4/15/2015 42.5 38.05 4/16/2015 42.5 38.2 4/17/2015 42.45 38.1 4/20/2015 42.35 38.1 4/21/2015 42.35 38.15 4/22/2015 42.5 38 4/23/2015 42.35 37.95 4/24/2015 42.4 37.9 4/27/2015 42.35 37.8 4/28/2015 42.55 37.95 4/29/2015 42.5 37.9 4/30/2015 42.55 37.85 5/1/2015 42.55 38.3 5/4/2015 42.95 38.3 5/5/2015 42.9 38.2 5/6/2015 43.05 38.4 5/7/2015 44.35 38.55 5/8/2015 41.9 38.2 5/11/2015 42.2 38.1 5/12/2015 42.95 38.05 5/13/2015 43.2 38.3 5/14/2015 42.9 38.35 5/15/2015 43 38.65 5/18/2015 43 38.65 5/19/2015 43 38.65 5/20/2015 42.95 38.6 5/21/2015 43.05 38.9 5/22/2015 43 38.75 5/25/2015 42.4 39 5/26/2015 42.55 38.75 5/27/2015 42.5 38.7 5/28/2015 41.8 38.1 5/29/2015 41.75 38 6/1/2015 43.65 38.15 6/2/2015 42 38.2 6/3/2015 40.6 38.05 6/4/2015 41.95 37.9 6/5/2015 41.9 37.85 6/8/2015 42.1 38.35 6/9/2015 42.15 38.45 6/10/2015 6/11/2015 6/12/2015 6/15/2015 6/16/2015 6/17/2015 6/18/2015 6/19/2015 6/22/2015 6/23/2015 6/24/2015 6/25/2015 6/26/2015 6/29/2015 6/30/2015 7/1/2015 7/2/2015 7/3/2015 7/6/2015 7/7/2015 7/8/2015 7/9/2015 7/10/2015 7/13/2015 7/14/2015 7/15/2015 7/16/2015 7/17/2015 7/20/2015 7/21/2015 7/22/2015 7/23/2015 7/24/2015 7/27/2015 7/28/2015 7/29/2015 7/30/2015 7/31/2015 8/3/2015 8/4/2015 8/5/2015 8/6/2015 8/7/2015 8/10/2015 8/11/2015 8/12/2015 42.25 42 41.8 42.15 42.15 40.8 42 41.5 41.55 41.9 41.5 41.15 41.15 41.35 41.15 41.95 46.5 41.65 41.25 42.3 42.1 41.9 42.3 41.05 42.4 42.5 41.95 42.25 41.5 41.55 41.75 41.95 41.85 42.2 42.1 42.1 41.95 42 41.1 40.8 41.45 41.6 40.4 40.85 41.75 41.6 38.7 38.5 38.35 38.55 38.5 38.35 38.3 37.85 37.75 37.75 37.8 37.7 37.6 37.55 37.65 38.05 37.8 37.7 38.15 37.7 37.7 37.75 37.85 37.8 37.8 37.85 37.65 37.65 37.75 37.65 37.65 38.2 38.2 38.1 38.15 38.35 38.45 38.35 38.25 38.05 38.15 38.1 38.05 38.05 38.05 38 8/13/2015 8/14/2015 8/17/2015 8/18/2015 8/19/2015 8/20/2015 8/21/2015 8/24/2015 8/25/2015 8/26/2015 8/27/2015 8/28/2015 8/31/2015 9/1/2015 9/2/2015 9/3/2015 9/4/2015 9/7/2015 9/8/2015 9/9/2015 9/10/2015 9/11/2015 9/14/2015 9/15/2015 9/16/2015 9/17/2015 9/18/2015 9/21/2015 9/22/2015 9/23/2015 9/24/2015 9/25/2015 9/28/2015 9/29/2015 9/30/2015 10/1/2015 10/2/2015 10/5/2015 10/6/2015 10/7/2015 10/8/2015 10/9/2015 10/12/2015 10/13/2015 10/14/2015 10/15/2015 41.3 41.15 41.2 41.2 41.1 41.3 41.65 41.35 41.6 42.65 42.55 41.85 40.7 42.05 41.35 41.55 41.7 41.65 42.05 41.85 42 42.2 41.8 42.3 42.2 42.2 41.15 41.5 41.4 40.3 40.3 39.1 40.6 40.35 40.05 40 39.7 39.8 39.75 39.75 39.75 39.8 39.9 39.8 40.05 39.85 38.1 37.8 37.9 37.85 37.6 38.15 38.15 38.15 38.3 41.55 41.55 38.05 38.2 38.25 38.25 38.2 38.3 38.3 38.2 38.45 38.45 38.45 38.45 38.55 38.35 38.4 38.4 38.4 38.15 37.8 37.5 37.1 36.8 36.75 36.75 36.35 36.05 35.95 35.95 36 36 36.1 36 36 36 35.85 10/16/2015 10/19/2015 10/20/2015 10/21/2015 10/22/2015 10/23/2015 10/26/2015 10/27/2015 10/28/2015 10/29/2015 10/30/2015 11/2/2015 11/3/2015 11/4/2015 11/5/2015 11/6/2015 11/9/2015 11/10/2015 11/11/2015 11/12/2015 11/13/2015 11/16/2015 11/17/2015 11/18/2015 11/19/2015 11/20/2015 11/23/2015 11/24/2015 11/25/2015 11/26/2015 11/27/2015 11/30/2015 12/1/2015 12/2/2015 12/3/2015 12/4/2015 12/7/2015 12/8/2015 12/9/2015 12/10/2015 12/11/2015 12/14/2015 12/15/2015 12/16/2015 12/17/2015 12/18/2015 39.75 39.95 39.9 39.75 39.85 39.65 38.95 39.15 38.55 38.6 38.65 38.35 38.55 38.6 38.6 38.45 38.3 38.3 38.15 38.05 38.4 38.35 38.35 38.3 38.2 37.55 37.5 37.35 37.4 37.35 37.4 37.2 36.75 36.7 36.95 37.05 36.8 36.65 37 37 37.1 36.9 36.7 37.1 37.55 38.35 35.95 35.95 35.95 36.05 36.1 36.05 35.65 35.4 35.25 34.8 35.1 35.05 34.7 34.6 34.75 34.9 34.8 34.7 34.6 34.55 34.5 34.55 34.65 34.6 34.55 34.25 33.7 33.8 33.65 33.6 33.7 33.65 33.45 33.1 34.5 33.6 33.5 33.55 33.75 34 34 34 33.75 33.9 34.5 34.95 12/21/2015 12/22/2015 12/23/2015 12/24/2015 12/25/2015 12/28/2015 12/29/2015 12/30/2015 12/31/2015 1/1/2016 1/4/2016 1/5/2016 1/6/2016 1/7/2016 1/8/2016 1/11/2016 1/12/2016 1/13/2016 1/14/2016 1/15/2016 1/18/2016 1/19/2016 1/20/2016 1/21/2016 1/22/2016 1/25/2016 1/26/2016 1/27/2016 1/28/2016 1/29/2016 2/1/2016 2/2/2016 2/3/2016 2/4/2016 2/5/2016 2/8/2016 2/9/2016 2/10/2016 2/11/2016 2/12/2016 2/15/2016 2/16/2016 2/17/2016 2/18/2016 2/19/2016 2/22/2016 38.7 38.6 38.95 38.75 38.9 39.3 39.75 39.15 39.6 39.6 39.25 39.25 39 39.25 39.55 39.65 39.7 38.8 38.55 37.6 37.5 37.4 37.4 37.3 37.3 37.55 37.7 37.55 37.55 37.8 38.25 37.65 37.4 37.4 37.45 37.85 38.15 38.15 38 37.95 37.95 37.95 37.7 37.6 37.4 37.35 35.25 35.5 35.85 35.7 35.65 35.65 35.65 36.45 36.15 36 36 36.15 35.65 35.65 36 35.95 35.55 34.9 34.4 33.6 33.65 33.5 33.65 33.5 33.45 33.7 33.8 33.65 33.8 34.05 34.15 33.6 33.45 33.4 33.7 33.9 34.2 34.15 33.8 33.8 33.9 33.85 33.7 33.4 33.35 33.35 2/23/2016 2/24/2016 2/25/2016 2/26/2016 2/29/2016 3/1/2016 3/2/2016 3/3/2016 3/4/2016 3/7/2016 3/8/2016 3/9/2016 3/10/2016 3/11/2016 3/14/2016 3/15/2016 3/16/2016 3/17/2016 3/18/2016 3/21/2016 3/22/2016 3/23/2016 3/24/2016 3/25/2016 3/28/2016 3/29/2016 3/30/2016 3/31/2016 4/1/2016 4/4/2016 4/5/2016 4/6/2016 4/7/2016 4/8/2016 37.2 36.75 36.75 36.65 36.9 36.65 37.4 37.3 37.3 37.55 37.5 37.5 37.7 38.55 38.9 39 39 39.15 39.65 39.65 38.7 38.85 38.35 38.35 38.6 38.45 38.5 38.5 38.15 38.15 38.3 38.05 37.75 38.05 33.2 32.85 32.8 32.85 33.05 33.1 33.65 33.35 33.4 33.45 33.4 33.4 33.75 34.35 34.5 34.65 34.65 35 35.2 35.05 34.5 34.45 34.15 34.05 34.25 34.25 34.2 33.95 33.9 33.9 33.95 33.8 33.5 33.65 Project 3 Due May 13, 2015 In this project you are going to examine revenue putsa currently popular hedge for project finance of generation. The following is a substantially simplified versionin practice both the asset and the revenue put involve simulation and exercise mechanics at the hourly time-scale, often at highly illiquid delivery locations. Setup: The trade date is 08Apr2016. We will start with the hedgethe revenue put. Consider the following derivative version of a generator. Heat rate: 7.2 VOM: $5/MWh Capacity: 800MW Electricity price: PJM Western Hub. Natural gas price: TETM3 Also: 1. We will only focus on the delivery month of Dec2016 and the on peak (5x16) delivery bucket. This means that the maximum generation output (total notional) is product of the capacity, 16 hours per day and the 21 peak delivery days in the month. 2. For simplicity we will also assume that this generator is simply a monthly call option on the spread: F (Te ) HG(Te ) K, where: - Te corresponding to the expiration date 29Nov2016 (two business days before the month); - F and G are the Dec16 forward prices of electricity and natural gas respectively; - H and K are the generator heat rate and VOM respectively. On the trade date: Power forward: F = 38.05 $/MWh. Gas forward: G = 2.956 $/MMBtu Power implied vol: .40. Gas implied vol: .35. 1 Part I Your goal is to analyze a put on the payoff of this generator struck at L = $1.5 million. Proceed as follows: 1. Generate a set of two independent standard normal deviates of size 1000. Consider this a random vector Z of size 1000x2. 2. For a grid of correlations spanning .5 to .95 by steps of say .05: (Note: Compute correlated standard normal returns Y from Z. Do Step 1 once, so that you have the same set Z for all subsequent calculations; do not resimulate Z for each correlation value). You can do this by applying the square root of the covariance matrix p to Z or simply by letting: Y1 = Z1 and Y2 = Z1 + 1 2 Z2 . Generate log normal simulations for F (Te ) and G(Te ) using the implied vols given above. Calculate the resulting generation value simulations: V N max [F (Te ) HG(Te ) K, 0] where N is the total notional. Compute the simulated payoffs of the revenue put: min [L V, 0]. 3. Plot the expected generation value versus correlation. Do the same for the put values and explain why this result is reasonable. Part II A put of the form above is often referred to as a revenue put. Its purpose is to put a floor on the value of a generator against which money is borrowed to finance its construction or purchase. We will now assume that the asset being hedged by the revenue put above is identical in form except that it is built in a location where it will receive another power price (ADHUB in Ohio). The goal is to analyze just how effectively the revenue put in Part I hedges an asset at this different delivery location. We will depart from the usual GBM modeling in dealing with this new location. Otherwise we would have to estimate returns correlations between all three underlying prices: PJMWH, TETM3 and ADHUB and somehow also estimate the implied vol at ADHUB which does not trade. Moreover, in practice, the asset is often at a location that has no forward price data and more detailed analysis of hourly spot prices is required. To this end, the attached spreadsheet Project3 Data.xlsx has by trade date historical Dec16 forward prices for PJMWH and ADHUB. 1. Make a scatter plot of ADHUB (F ) versus PJMWH (F ). 2 2. Identify and remove obvious outliers and linearly regress F against F . 3. Compute simulations for F (PJMWH) as in Part 1 using a correlation of .70. 4. Generate simulations for F by using the simulations for F along with the linear model: where: - F (Te ) = a + bF (Te ) + Z. - [a, b] are the regression coefficients. - is the standard deviation of the residuals from the regression. - Z is another independent simulation of 1000 standard normal deviates. Note: This model assumes that the residuals at expiry are uncorrelated with their current value at the trade date. More advanced time series methods could clearly be used if needed. 5. Using the simulations for F calculate the ADHUB generation values: i h V N max F (Te ) HG(Te ) K, 0 6. Make a histogram of V and another histogram of V + (the sum of the ADHUB asset simulations and the revenue put simulations from Part I). The latter is the hedged portfolio. 7. What is the 5th percentile of the hedged portfolio and why is it less than the strike of $1.5m? How would you modify the revenue put structure (qualitatively) to bring the 5th percentile closer to the desired level of $1.5m? 3