Valuation of Exotic Options and Counterparty Games Based on Conditional Diffusion

Options and structured products, as pivotal financial derivatives, provide contract holders with specific payoff structures based on the performance of underlying assets at predetermined times and conditions. They serve as effective tools for investment institutions to manage risk, hedge exposures, and optimize investment portfolios. With the continuous development of financial markets and the diversification of investor demands, financial institutions have invented a wide variety of exotic options based on the principles and experience of standard options. Exotic options can be further categorized according to their complexity: relatively simple exotic options such as Asian options, barrier options, lookback options, and ratchet options primarily add a single feature to standard options; while highly complex structured products like snowball products, phoenix notes, shark fin options, and cumulative products feature multiple path-dependent conditions and intricate payoff structures. These innovative financial instruments not only broaden investor choices but also provide powerful tools for more refined and personalized risk management and investment strategies[1]. Precisely because exotic options and structured products exhibit high levels of diversity, customization, and structural complexity, accurate pricing remains a core challenge for all market participants.