Company N experienced a negative impact on their business due to the covid pandemic with a result of unexpected financial losses. Company N implemented some financial strategies to deal with the issues. However, in October $2022,$ businesses in UK$,$ Europe and Japan faced more financial uncertainties due to the aggressive US interest rate hikes. The government and the central bank of Japan were concerns about the currency sharp declines. Within a week they intervene in the currency market to stem yen weakness by selling dollars and buying yen for the first time since $1998.$ The yens recent sharp declines, which have increased living costs by boosting imported fuel and food prices, have been driven in part by widening divergence between the U$.$S$.$s aggressive monetary tightening and the Japans ultra$-$loose monetary policy. On Monday the dollar added $0\mathrm{.}35\%$ to $\yen 149\mathrm{.}58,4$ continuing its climb back towards last Thursday $24-$year peak of $\yen 155\mathrm{.}37.$ It tumbled to $\yen 143\mathrm{.}58$ that same day after Japanese authorities involved in the market. While government officials jawboning may keep markets nervous of the prospect of further intervention, stepping in repeatedly in the currency market and selling huge sums of dollars could be difficult due to the criticism Japan may face from its Group of Seven counterparts. it is unlikely Japan will continue intervening to defend a certain line, such as $\yen 152\mathrm{.}50$ to the dollar, former top Japanese currency diplomat told Reuters. Other currencies like the British pound, the euro and the Chinese yuan were also affected by the aggressive interest rate increases.

a$)$ What can be inferred about the level of interest rate in Japan relative to the level of interest rate in the US$?$

b$)$ Does the International Fisher E$\mathrm{}$ffect hold? Why?

c$)$ If International Fisher Effect does not hold, which theory can explain the Yen exchange rate?

d$)$ Identify and explain two speculative trading strategies using currency derivatives to benefit from the yen depreciation against the dollar.

e$)$ Explain the outcome of these strategies if the central bank of Japan intervene in the forex market?