The JIBAR futures contract trading on SAFEX closely resembles the EURIBOR contract trading in European markets $($and the now defunct Eurodollar contract$),$ except that the underlying asset is $3-$month JIBAR $($i$.$e$.$ ZAR rates$)$ and not $3-$month EURIBOR $($i$.$e$.$ EUR rates$).$ The following reflects the actual JIBAR futures contract details as traded on SAFEX:

$$ Contract base $($i$.$e$.$ underlying asset$)$: $3-$month JIBAR rate

$$ Contract notional amount: ZAR $100000$ face value.

$$ Quotation style: The $3-$month JIBAR futures are quoted in the same way as the

underlying JIBAR rate, namely on a yield basis. The price is determined from the yield

using the formula: $100$ yield.

$$ In this module, JIBAR futures can be quoted as follows:

$$ a$)$price$$ or $$IMM index$$ format $($i$.$e$.$ index of $100$ yield, where $$yield$$ is a

nominal annual rate $[$i$.$e$.$ NACQ$])$; or

$$ b$)$yield$$ format $($i$.$e$.$ quoting the futures as a Nominal Annual Rate $($NACQ$)).$

$$ The JIBAR futures in Table $3\mathrm{.}2.$ are quoted on a $$price$$ basis $($i$.$e$.$ IMM index$).$

$$ Contract months: March, June, September, December and $$serial contracts$($i$.$e$.$ four

near$-$term contracts to ensure six consecutive near months is listed. In this module, not

all contracts might be provided.

$360$ day$-$count is used.

$$ Basis point value: ZAR $2\mathrm{.}50$ per basis point $($in NACQ format$)$ per contract $($i$.$e$.$ R$100000$ x $0\mathrm{.}0001$ x $(90/360))$

$$ Settlement: Cash

Suppose the following spot interest rates $($Table $1)$ and JIBAR futures contracts $($Table $2)$ are

quoted on $1$ December $2023($i$.$e$.14$ days before the December $2023$ contract expires$).$ Table $1$: JIBAR Spot rates $($NAC$)$ on $1$ December $2023$:

JIBAR $14-$day rate: JIBAR $44-$day rate: JIBAR $58-$day rate: JIBAR $74-$day rate: JIBAR $90-$day rate: JIBAR $104-$day rate: JIBAR $134-$day rate: JIBAR $164-$day rate: JIBAR $180-$day rate: JIBAR $194-$day rate: JIBAR $224-$day rate: JIBAR $254-$day rate: JIBAR $270-$day rate:

$7\mathrm{.}9000\%7\mathrm{.}9200\%7\mathrm{.}9300\%7\mathrm{.}9500\%7\mathrm{.}9700\%7\mathrm{.}9900\%8\mathrm{.}0200\%8\mathrm{.}1200\%8\mathrm{.}1500\%8\mathrm{.}1700\%8\mathrm{.}2200\%8\mathrm{.}2300\%8\mathrm{.}2400\%$

Table $2$: JIBAR Futures contract prices on $1$ December $2023$:

December $152023($expiration in $14$ days$)$: January $152024($expiration in $44$ days$)$: February $152024($expiration in $74$ days$)$: March $152024($expiration in $104$ days$)$: April $152024($expiration in $134$ days$)$:

$92\mathrm{.}020592\mathrm{.}008591\mathrm{.}497091\mathrm{.}811091\mathrm{.}7291$

Note: Initial Margin required per JIBAR contract $=$ R$220$

$1\mathrm{.}1$ Calculate the yields $($i$.$e$.$ NACQ$)$ for the Dec $2023$ and April $2024$ futures contracts. $(4)$

$1\mathrm{.}2$ Calculate the implicit price $($per R$100000$ face value$)$ that is currently quoted for the February $2024$ JIBAR futures contract. $(2)$

$1\mathrm{.}3$ As an arbitrage specialist, you suspect that the February $2024$ JIBAR futures contract in Table $2$ might be incorrectly priced. Prove that the February $2024$ contract is mispriced. $(5)$

$1\mathrm{.}4$ Explain, in detail, what arbitrage transactions you will undertake to exploit the mispricing. Assume the February $2024$ JIBAR futures contract is priced at and index level of $91\mathrm{.}100$ on expiration date $(15$ Feb $2024).$ Note: use $360$ day$-$count throughout

and ignore margin requirement calculations for this question.