Case study $4$

An investment company decided to use equity options to hedge an investment of $525000$ shares

in MNL Plc on the market on $15$th July $2021.$

MNL Plc$$s share price on $15$th July was $482$ pence

Option premiums and annualised implied price volatilities for MNL shares were:

Option Premiums $($Pence Per Share$)$ Annualised Implied Volatility

Exercise Price Calls Puts

$47020\mathrm{.}077\mathrm{.}460\mathrm{.}1622$

$48014\mathrm{.}2311\mathrm{.}610\mathrm{.}1617$

$4909\mathrm{.}6116\mathrm{.}970\mathrm{.}161$

And:

$$ The risk$-$free rate of return was $0\mathrm{.}0075$

$$ The exercise date for the options was $15$th September

$$ A single traded option contract is for $1000$ MNL Plc shares

Required

a$)$ Compute how much the investment in MNL Plc was worth on $15$th July and briefly characterise the risk that the Investment

company decided to hedge with options. $(3$ marks$)$

b$)$ Construct the delta$-$hedge that Investment would have established on $15$th July using the nearest to at$-$the$-$money contract.

Explain your reasoning. $($You can assume that MNL shares are non$-$dividend paying$).(7$ marks$)$

c$)$ Demonstrate and critically discuss how effectively the hedge works if MNL$$s share price immediately falls to $443$ pence

$(7$ marks$)$

d$)$ Show how the hedge should be adjusted to maintain delta neutrality.

$(4$ marks$)$

e$)$ Gama is $0\mathrm{.}01210$ Demonstrate the significance of gamma for maintaining a delta$-$neutral hedge.

$(4$ marks$)$

$($Total $25$ marks$)$