The JIBAR futures contract trading on SAFE 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:

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$$

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 $0\mathrm{.}0001\backslash$times $(90/360))$

$$ Settlement: Cash

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

$7\mathrm{.}9000\%$

JIBAR $44-$day rate:$7\mathrm{.}9200\%$

JIBAR $58-$day rate:$7\mathrm{.}9300\%$

JIBAR $74-$day rate:$7\mathrm{.}9500\%$

JIBAR $90-$dav rate:

$7\mathrm{.}9700\%$

JIBAR $104-$day rate:$7\mathrm{.}9900\%$

JIBAR $134-$day rate:$8\mathrm{.}0200\%$

JIBAR $164-$day rate:$8\mathrm{.}1200\%$

JIBAR $180-$day rate:$8\mathrm{.}1500\%$

JIBAR $194-$day rate:$8\mathrm{.}1700\%$

JIBAR $224-$day rate:$8\mathrm{.}2200\%$

JIBAR $254-$day rate:$8\mathrm{.}2300\%$

JIBAR $270-$day rate:$8\mathrm{.}2400\%$

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

December $152023($expiration in $14$ days$)$:

$92\mathrm{.}0205$

January $152024($expiration in $44$ days$)$:

$92\mathrm{.}0085$

February $152024($expiration in $74$ days$)$:$91\mathrm{.}4970$

March $152024($expiration in $104$ days$)$:$91\mathrm{.}8110$

April $152024($expiration in $134$ days$)$:

$91\mathrm{.}7291$

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.

$(9)$