Exposure Profile Example
Monte Carlo simulation lies at the heart of the Open Source Risk Engine (ORE).
It requires a vast array of pricing and simulation models for complex derivatives, structured products, and cash instruments. The first step in ORE’s portfolio risk analysis requires the simulation of relevant factors that affect the price of each trade out into the future using Risk Factor Evolution (RFE) models over many random scenarios. Typical RFE models project interest rates, foreign exchange rates, consumer price indices and real rates, default and recovery rates, equity prices, and commodity prices, while also taking into account the volatility and correlation of these risk factors.
The next step requires the revaluation of each trade at every future point and scenario using product-specific pricing models according to the type of trade, such as a vanilla interest rate swap or cross-currency swap. An efficient simulation must handle thousands of trades across thousands of scenarios and many future evaluation dates: to give some perspective, typical dimensions for a portfolio could include 10,000 trades, 120 evaluation dates (quarterly time steps over the next 30 years), and 10,000 market scenarios. That data cube (trades x dates x scenarios) alone would contain 12 billion prices! If pricing a single trade took an average of 50 microseconds, the calculations in this example would require around 170 CPU hours on a single-core machine or two and a half hours on 64 cores.
Ultimately, the Monte Carlo framework provides a set of future (simulated) net present values (NPVs) for the portfolio under randomly-generated market scenarios. ORE then calculates an average of the positive (EPE) and negative (ENE) exposures, as well as a quantile (PFE) of the future positive exposure, and these values are displayed within the Exposure Profile chart of the Risk Dashboard. Careful analysis of these exposure profiles can tell the user much about the trade’s characteristics. See some examples below:
Mismatched coupon payments result in “jagged” exposure profiles.
A / CUST_J / CSA_50 / Trade_4651
Trade_4651 has a small positive NPV on June 30, 2015 ($1,055), meaning that from the perspective of the user the trade is “in-the-money” (i.e. counterparty owes user). However, this trade NPV eventually becomes negative over the course of the following year ending July 6, 2016 (-$6,206) as seen in the Total Exposure chart. At June 30, 2016, given its relatively small NPV, the EPE and ENE profiles in the Exposure Profile chart are close to mirror images of each other over the x-axis, signifying that the future evolution of the trade’s NPV has an almost equal chance of staying positive or becoming negative over the remaining 5 years until maturity on June 30, 2020.
The EPE and ENE lines are examples of a “jagged” exposure profile, which indicates a mismatch in the timing of interest payments between the two counterparties. In this instance, user is a 6-month fixed rate receiver and 3-month floating rate payer, meaning that EPE spikes every 6 months while ENE declines at the same time as user anticipates receiving the interest payment from the counterparty, then falling the subsequent quarter after payment is made. Thus, you can infer that the fixed rate payment is received between January 31-March 31 and June 30-September 30 each year. Use the slider below each chart to zoom in specific date rangers for shorter maturities, as below.
By July 6, 2016 the NPV has become dramatically more negative, and the exposure profiles change to account for the lower probability that the trade becomes positive over the remaining maturity. This is seen in the much smaller EPE and PFE profiles well below the ~$5,000 and ~$18,000 peaks, respectively, on June 30, 2015.
A / CUST_Y / CSA_121 / Trade_1985
Trade_1985 has similar characteristics as the previous examples with some important differences that account for a slightly different shape in the exposure profile. As before, this trade begins with a small positive NPV on June 30, 2016 that grows larger and more dramatically negative by July 6, 2016. However, you can see the longer remaining maturity in this example (13 years vs. only 5 years previously), as well as “spikes” in the exposure profile that are more spaced out than the previous example due to user being a 1-year fixed rate payer and 3-month floating rate receiver. Thus, EPE and PFE increase as the user’s payment is made annually (as opposed to every 6 months in the previous example), while ENE (the counterparty’s exposure to the user) declines at the same time.
On July 6, 2016, as in the previous example, the NPV becomes significantly more negative causing the exposure profiles change to account for the lower probability that the trade becomes positive over the remaining maturity. This is seen in the much smaller EPE and PFE profiles well below the ~$10,000 and ~$40,000 peaks, respectively, on June 30, 2015.
Long-dated, deep “in-the-money” NPV results in limited ENE profile
C / CUST_I / CSA_41 / Trade_1369
Trade_1369 is a long-dated (20+ year), deep in-the-money swap as evidenced by the very large positive NPV on June 30, 2016. User is a 1-year fixed rate receiver and 6-month floating rate payer.
The large positive NPV has a dramatic effect on the exposure profiles due to the lack of a significant ENE profile, meaning that the trade has a very low probability of ever having a negative NPV from the perspective of the user. Due to the user only receiving one interest payment annually, the EPE profile grows for three consecutive quarters before declining after the interest payment is received between March 31 and June 30 each year.
AA / CUST_D / CSA_16 / Trade_6405
Trade_6405 demonstrates matched coupon payments, as the user is a 6-month fixed rate receiver and 6-month floating rate payer. On June 30, 2015, notice flat EPE and ENE profiles with lack of any “spikes” as in previous examples, caused by the simultaneous exchange of interest payments. Given the relatively small NPV on this date, an ENE profile emerges due to the long-dated maturity (20+ years) meaning the trade still has plenty of time to turn into a negative NPV. However, by July 6, 2016, the trade’s NPV has grown to almost $4,000 and the ENE profile is no longer significant.