Use the information in the following table to determine the lower bound of the

August $160$ put option assuming European options. The option prices were

observed for a stock on July $6$ of a particular year. Ignore dividends on the stock.

The stock is priced at $$165\mathrm{.}13.$ The expirations are August $21$ and October $16.$ The

risk free rates are $5$:$50\%$ for August and $5\mathrm{.}88\%$ for October.

Calls

Puts

Strike Aug Oct Aug Oct

$$155$ $$11\mathrm{.}80,$$$14\mathrm{.}00,$$$1\mathrm{.}25,$$$2\mathrm{.}75$

$\{\begin{array}{ccc}\text{:}[\text{\$}160,& \text{\$}8\mathrm{.}10,\text{\$}11\mathrm{.}10,& \text{\$}2\mathrm{.}75]\end{array}$$$4\mathrm{.}50$

$\{\begin{array}{ccc}\text{:}[\text{\$}165,& \text{\$}5\mathrm{.}20,\text{\$}8\mathrm{.}10,& \text{\$}4\mathrm{.}70]\end{array}$$$$6\mathrm{.}70$

$\{\begin{array}{ccc}\text{:}[\text{\$}170,& \text{\$}3\mathrm{.}20,\text{\$}6\mathrm{.}00,& \text{\$}7\mathrm{.}50]\end{array}$$$9\mathrm{.}00$

$$2\mathrm{.}18$

$$0$

$$5\mathrm{.}37$

$$2\mathrm{.}75$