Double Dice Ltd$.,$ a burgeoning Quebec company excelling in crafting bespoke

footwear, has recently welcomed you aboard as a financial analyst. Given that the

team at Double Dice lacks fundamental knowledge about financial options, you have

been tasked with drafting a concise report to enlighten the firm's executives on the

basics. Initially, you scoured external resources on the topic and formulated a list of

relevant questions that need addressing. A potential structure for the report could

be a question$-$and$-$answer format. With the questions ready, it's time to formulate

the answers. $-31\mathrm{.}12$

Part $($a$)$: A share is in play at $40,$ flaunting a $4\%$ continuous dividend yield and $22\%$

annualized volatility. A one$-$year call option on this share sports a strike price of

$36.$ The continuous risk$-$free rate is $2\mathrm{.}5\%.$ Risk factors are: $d1=0\mathrm{.}560,N(d1)=$

$0\mathrm{.}713,d2=0\mathrm{.}360,N(d2)=0\mathrm{.}640.$ Use the Black$-$Scholes$-$Merton model to compute

the value of the call option. $(2\mathrm{.}5$ Marks$)$

Part $($b$)$: How do the ensuing call option parameters impact the value of a put

option? $(5$ Marks$)$

$(1)$ Present stock price

$(2)$ Strike price

$(3)$ Option's tenure to maturity

$(4)$ Volatility of the stock price

$(5)$ Level of interest rates

Part $($c$)$: Unveil the enigma of put$-$call parity. James is on a quest to ascertain the fair

value of a put option with a strike price of $$18,$ set to expire in $2$ years. A call bearing

the identical strike price and expiration is valued at $$6.$ The risk$-$free rate is $4\mathrm{.}5\%.$

The Spot Price of the underlying asset stands at $$20.$ Employing Put $-$ Call Parity,

unravel the fair value of the put option? $($Assume continuous compounding$)(2\mathrm{.}5$

Marks$)$Part $($d$)$: In $1973,$ the dynamic duo of Fischer Black and Myron Scholes birthed the

Black$-$Scholes option$-$pricing model $($OPM$).$ Could you provide the assumptions that

underpin the OPM? $(5$ Marks$)$

Part $($e$)$: Imagine $90-$day ventures in Britain promise a $7\%$ annualized return and a

$1\mathrm{.}75\%$ quarterly $(90-$day$)$ return. Meanwhile, in Canada, similar risk $90-$day

ventures offer a $5\%$ annualized return and a $1\mathrm{.}25\%$ quarterly $(90-$day$)$ return. In the

$90-$day forward market, $1$ British pound equals $$2\mathrm{.}10.$

If interest rate parity holds true, what's the spot exchange rate? $(5$ Marks$)$

Part $(f$ : The Bank of Canada $($BoC$)$ occasionally adjusts the key policy interest rate

to maintain price stability and support economic growth. Assume you are an analyst

at a financial advisory firm. Your client is concerned about the impact of a potential

interest rate hike on their bond portfolio. Explain how a rise in interest rates could

affect bond prices and what steps your client could take to mitigate the risks

associated with rising interest rates. $(5$ Marks$)$

If interest rate parity holds true, what's the spot exchange rate? $(5$ Marks$)$