Deposit Futures

## Deposit Futures

Deposit futures is technically similar to an FRA contract with respect to pricing and valuation. In Malaysia, 3M KLIBOR futures is a deposit futures available for trading and dominated by financial institutions managing its long term interest rate exposure.

The 3-month KLIBOR futures contract is a forward borrowing and lending contract albeit several differences compared to an FRA. Some of these differences are compared in Table 2-5.

Table 2-5

The 3M KLIBOR futures shares the same specification with the Eurodollar 3M LIBOR futures except for the denominated currency and expiry dates. For comparison, some of the features for these contracts are listed in the Table 2-6.

Table 2-6

Table 2-7 listed sample contracts for 3M KLIBOR futures and their prices.

Table 2-7

Prices quoted for futures contract in this case are not the proceed or present value of the contract. Instead, it is 100 - forward rate of the contract. U20, for instance is quoted as 96.95/97.05. In terms of forward rate, the quotation for U20 is 3.05%/2.95%. Buying a futures contract by taking the offer at 97.05 means that the buyer is a forward lender at a rate of 2.95%.

At the close of the day, the exchange will mark to market all open position. If the settlement price at the close is 97.06, the buyer has a profit of MYR25 while the seller of the contract will have a loss of MYR25. The amount will be credited to the buyer’s account held with the futures broking house, while the seller will be debited for his loss.

On the third Wednesday of September 2020, the contract will expire and the 3M KLIBOR will be used as the reference rate for settlement. If 3M KLIBOR is fixed at 2.80% , then the settlement price for the U20 will be 97.20. The total profit to the original buyer at 97.05 is (97.20-97.05) x 100 x MYR25 = MYR375. The seller, on the other hand will lose the equivalent amount.

### Tick Value and Convexity Adjustment

3M KLIBOR futures contract has a tick value of MYR25 which is determined by the exchange. The tick value is derived from the assumptions:

1. that the futures contract is a 3-month or a 90-day contract;
2. the value of 1 basis point is not discounted to present value; and
3. interest of the futures contract is calculated as:
1. Face Value x 3 months/12 months similar to Equation 1-1; or
2. Face Value x 90 days/360 days based on 30/360 convention.
Both iii.a or iii.b will yield the same tick value. For our illustration, iii.a will be used and the tick value can be calculated in the following manner.

\begin{align} \textrm{Tick Value}&=\textrm{1,000,000 x }\frac{3}{12} \\ &=25 \end{align}

Regardless of how far the expiry of the futures from today, the tick value of a futures contract remains at 25 i.e U20, Z20, H21 and M21 in Table 2-7 have the same tick value of 25.

PVBP01 of an FRA, on the other hand decreases as the expiry of the contract gets further away from current date due to convexity. Consequently, pricing of other interest rate products using 3M KLIBOR futures will be inaccurate due to the its constant tick value or PVBP01. Convexity adjustment has to be made to the pricing of any financial products using rates implied by the futures contract.

Convexity adjustment is discussed in Chapter 29 of “Options, Futures and Other Derivatives”, 7$$^{\textrm{th}}$$ Edition by John C Hull. In essence, the convexity adjustment can be approximated by:

\begin{align} ca &= 0.5\sigma^2T_1T_2\\ \textrm{where }ca&=\textrm{ convexity adjustment} \\ \sigma &= \textrm{ volatility of the futures contract} \\ T_1 &= \textrm{ time in years to the expiry date of the contract} \\ T_2 &= \textrm{ time in years to the theoretical maturity date of the contract which is } T_1 + \dfrac{90}{360} \end{align}

Equation 2-4

There several steps before getting the forward rate from the futures price.

1. Convert the futures price to rate
2. Convert the rate to equivalent continuous rate
4. Deduct (iii) from (ii) to get the continuous forward rate
5. Convert the continuous forward rate to required type of rate

Calculator for convexity adjustment are provided and the relevant fields are described/explained below.

###### Expiry Date

Expiry date or last trading date of the futures contract.

###### Tenor

Tenor of the contract. Either a 90-day or 3-month contract can be chosen.

###### Theoretical Maturity Date

Calculated based on input in 'Expiry Date' and 'Tenor'.

###### Futures Price

Price of the futures contract.

###### Implied Futures Rate (%)

Calculated based on the 'Futures Price' input by user.

###### Implied Fut. Cont. Rate (%)

The equivalent continuous rate for the 'Implied Futures Rate (%)'. This is a calculated field

###### Convention

The day count convention applicable to the future contract. The information is used to calculated the day count factor, discount factor and subsequently convert the rate to continuous equivalent

###### Volatility (%)

Volatility of the futures contract

The convexity adjustment for the futures price. This is a calculated field.

###### Imp. Cont. Fwd Rate (%)

The implied continuous forward rate. This is a calculated field which is equivalent to 'Implied Fut. Cont. Rate (%)' less 'Convexity Adjustment'

###### Fwd Rate Convention

The day count convention used in calculating the 'Impled Forward Rate'.

###### Implied Forward Rate (%)

Implied forward rate from the futures price after taking into account convexity adjustment