Today, let’s expand our finance knowledge and study what HF portfolio managers and IB traders ‘constantly’ look at: *swaptions* and the implied interest rate volatility. A swaption, as you may know, is an option to enter an IRS (interest rate swap) with a specified rate at no cost on a future date.

For those who are not familiar with swaps, let’s review quickly the structure of a ‘vanilla’ IRS.

An IRS is a bilateral agreement to swap a fixed rate of interest for a floating rate of interest. It is a derivative contracts (traded OTC) and it involves two counterparties (at least), the fixed receiver (receives a fix rate) and the fixed payer (floating rate). Unlike currency swaps, principal amounts are not exchange in an IRS ‘vanilla’ contract, and only the difference between the fixed and the floating rate is paid/received. In order to trade (hedging/speculating), you need four parameters: the date, the notional amount, fixed rate and the floating rate.

At the inception of the swap, the Net Present Value or the sum of expected PnL should add up to zero. If you type IRS on Bloomberg, you get to the swap manager page that you can see below.

*(Source: Bloomberg)*

This contract is a 5-year IRS contract, 10Mio USD nominal between Leg 1 ‘Receiver’ and Leg 2 ‘Payer’. Therefore, with a fixed coupon of 1.796627% and October 10^{th} as the effective date (date when interest begins to accrue, the first fixed payment will occur 6 months after that date (on April 10 2014) totalling an amount of **89,831.35 USD**.

**Fixed rate payment = Fixed rate * (Nb Days / 360 basis) * Notional**

Nb of Days = 180, therefore Fixed Payment rate = 89,831.35 USD

On the other side, floating payments will occur every quarter, using the 3-month LIBOR as a benchmark (USD0003M Index). With a 3-month LIBOR trading at 0.23110% at the moment, the first floating-rate payment will occur on January 12 2014 (94 days) totalling an amount of **6,034.28 USD** (same computation as the Fixed –rate payment replacing Fixed rate by floating rate). On page 9 (Cashflow, see appendix), you will see all the future payment details.

As all the future payment of Leg 1(Fixed Receiver) will rely on the evolution of the forward LIBOR curve, the swap valuation changes over time and therefore existing swaps become **off-market swaps. **For the curious ones, you can easily find the math equation on Internet, but the important thing to remember is that the payer (Leg 2) will start to lose money if interest rate started to fall unexpectedly.

Here we are now, back to *swaptions* and the 1Y10Y implied volatility that we like to watch quite a bit. There are two kinds of *swaptions*, a payer *swaption* (option to pay fixed-rate, eq. to call option with PnL rising if rates are rising) and a receiver *swaption* (option to receive fixed-rate, eq. to a put option with PnL rising if rates are falling). If you buy a 1Y10Y 2% receiver *swaption*, it basically means that you have the right to receive a 2-percent rate on a 10 year basis starting in 1 year. Therefore, as we use the VIX in order to measure the market expectations of near-term volatility in the US stock market (S&P500), we use the 1Y10Y to ‘measure the temperature’ of the interest rate market. Quants use generally the Black’s model, a derived version of the Black and Scholes model (used for calls and puts), as a standard way of quoting prices on swaptions (two other methods of stochastic interpolation to model LIBOR forward rates are CEV and SABR.

If we have a look at 1Y10Y JPY implied volatility back in April/May 2013, we saw a surge in JPY volatility after the BoJ announced its QE plan which consists in doubling its monetary base within the next 2 fiscal years. As you can see it on the graph below, when the IR volatility (white/blue line) rose more than 60% in May, the ten-year JGB yield doubled and touched 1% (May 29^{th}), while Japanese stocks dropped 7% the same day with a USDJPY down 3 figures.

*(Source: Bloomberg)*

Investors are still concerned about the volatility of the bond market which would force domestic financial institutions to reduce their JGB holdings. As a reminder, more than 90% of the Japanese government debt is hold by domestic ‘investors’, and 95% of this amount is held by institutional investors (GPIF, Japan Post Bank.. and of course the BoJ). Domestic banks and small/midsize financial institutions account for more or less 29% now, and still remember the ‘VaR shock’ of summer 2003 when 10 JGB yield tripled from 0.5% to 1.6% in June.

According to a study done by JP Morgan [a little while ago], a rise in the ‘JGB volatility’ increasing interest rate by 100bps would cause a loss of 10Tr Yen for Japanese banks. Therefore, if you are holding a LT position on USDJPY or any other asset (bonds, equities), you should pay close attention to the forward curve and the 1Y10Y implied volatility we just presented you.

**Appendix: Cash Flows of the IRS**

*(Source: Bloomberg)*