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Тема На выбор:
(1) Arbitrage strategies. For example, arbitrage between futures contracts across different markets or options with different maturities or strike prices, etc
2) Hedging risk. For example, an airline company faces the risk of oil prices, it could use options or futures to hedge the risk, how to hedge the risk seems to be a technical problem, yet when is a more challenging problem.
(3) Pricing some complicated financial products embedded with options. For example, there were varieties of accumulators in the OTC markets, and terms in those accumulators with options could be very complicated. Pricing those derivatives using numerical approaches is challenging.
(4) Other topics related to financial derivatives. For example, you can discuss the question "why do stocks on Chinese A share market tend to have higher prices than their counterparts (H shares) in Hongkong stock market". Say, China petrol, a listed company in Shanghai stock market, is worth 5.7 Chinese Yuan, yet its H share price in Hongkong is only 4.13 Hongkong dollar which is almost 70% lower than its A share price (adjusted by exchange rate between Chinese Yuan and Hongkong dollar)