This thesis investigates the interaction between climate risk and financial markets, focusing on transition risk, physical risk, and their implications for asset pricing and hedging. Transition risk, stemming from the economic adjustments required to address climate change, is inherently challenging to quantify due to its reliance on regulatory and market dynamics. The study examines potential proxies, including European carbon allowance returns and a transition risk index, to measure transition risk in stock and bond markets. However, both proxies were found statistically insignificant, indicating limited sensitivity of financial markets to these variables or their inadequacy as measures of transition risk. Physical risk, caused by climate-related extreme events, demonstrated a more substantial influence on bond market pricing. A novel pricing model incorporating climate variables into the stochastic hazard rate framework was proposed, allowing for the assessment of physical risk exposure. This approach provided actionable insights for ranking corporate issuers based on their sensitivity to physical risk factors. The thesis also explores weather derivatives as hedging instruments for climate risk. For temperature-based derivatives, a market-aligned pricing model was introduced by defining a tradable "forward temperature" asset, addressing inefficiencies in existing methods. Despite these advances, the market for temperature derivatives remains underdeveloped, with significant underpricing. Additionally, innovative derivative contracts, such as Rainfall Quanto Options and Basin Level Cash-or-Nothing Options, were proposed to hedge water scarcity risks. These tools demonstrated effectiveness in addressing geographic and market limitations, offering flexibility beyond traditional insurance mechanisms. By analyzing the integration of climate risks into financial markets and proposing novel hedging instruments, this work provides valuable insights for policymakers, asset managers, and financial institutions to better assess, manage, and mitigate the financial impacts of climate change
