Suppose the following spot $($Table $1\mathrm{.}1)$ and futures contract $($Table $1\mathrm{.}2)$ interest rates on

JIBAR are quoted on $25$ August $2023($i$.$e$.20$ days before the September $2023$ contract expires$).$ Note that the spot rates are quoted as nominal annual $($NAC$)$ rates, while the futures rates are quoted as annual effective rates $($AER$).$

Table $1\mathrm{.}1$: JIBAR Spot rates $($NAC$)$ on $25$ August $2023$:

JIBAR $20-$day rate:

$6\mathrm{.}18\%$

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JIBAR $90-$day rate:

$6\mathrm{.}26\%$

tre forward

JIBAR $110-$day rate:

$6\mathrm{.}30\%$

JIBAR $180-$day rate:

$6\mathrm{.}61\%$

JIBAR $200-$dav rate:

$6\mathrm{.}72\%$

JIBAR $270-$day rate:

$7\mathrm{.}02\%$

JIBAR $290-$day rate:

$7\mathrm{.}07\%$

JIBAR $360-$day rate:

$7\mathrm{.}46\%$

JIBAR $380-$day rate:

$7\mathrm{.}53\%$

JIBAR $450-$day rate:

$7\mathrm{.}61\%$

JIBAR $470-$day rate:

$7\mathrm{.}68\%$

Table $1\mathrm{.}2$: JIBAR Futures contract prices $($IMM Index$)$ on $25$ August $2023$:

Actual

September $15,2023($expiration in $20$ days$)$:

$93\mathrm{.}6915$

December $15,2023($expiration in $110$ days$)$:

$92\mathrm{.}6775$

March $15,2024($expiration in $200$ days$)$:

$92\mathrm{.}4182$

June $15,2024($expiration in $290$ days$)$:

$91\mathrm{.}4712$

September $15,2024($expiration in $380$ days$)$:

$92\mathrm{.}2899$

Notes: Initial Margin required per JIBAR contract is R$100$

$1\mathrm{.}1$

$1\mathrm{.}2$

Calculate the yields $($i$.$e$.$ AER$)$ for the Dec $2023$ and June $2024$ futures contracts. $(6)$

Calculate the actual futures prices $($i$.$e$.$ PV of R$100000$ face value per JIBAR contract$)$ for both the Dec $2023$ and June $2024$ JIBAR futures contracts by discounting with the applicable NAC rates

$(6)$

$1\mathrm{.}3$

As an arbitrage specialist, you suspect that the December $2023$ and$/$or June $2024$

JIBAR futures contracts might be incorrectly priced. Calculate if any mispricing is present in the two contracts. Note $-$ use $360$ day$-$count throughout.

$(6)$

$1\mathrm{.}4$

Use the largest arbitrage opportunity in question $1\mathrm{.}3$ above and explain in detail what transactions you will undertake to exploit the mispricing.