A derivative is a financial instrument whose final payoff is derived from the value of one or more underlying assets. Naturally, in classical derivatives pricing causality is assumed to flow from the value of the underlying asset(s) to the value of the derivative. However, in the presence of certain frictions causality can reverse such that the derivatives market drives the underlying market instead of the other way around. I refer to instances of such reverse causality as derivatives feedback effects.
The literature distinguishes between informational and non-informational feedback effects (see, e.g., Ni et al. (2008) and Ni et al. (2020)). Informational feedback effects occur, for example, when the stock option market is quicker than the underlying stock market to process new information about the value of the underlying stocks. Non-informational feedback effects occur, for example, when the hedging transactions that derivatives dealers undertake are so large that they have a material impact on the price(s) of the underlying asset(s) (or the underlying market is not liquid enough to absorb such hedging trades without moving the price). Such feedback effects can increase or dampen volatility depending on the sign of derivatives dealers' convexity (in a sense that I make precise below). Loosely speaking: if we plot the total value of derivatives dealers' portfolios against the value of the underlying, does the curve bend upwards or downwards? If it bends downwards (negative convexity), then dealers' hedging activities tend to increase volatility and vice versa. For various reasons, dealers, as a group, often end up sitting on a negatively convex portfolio. The first two chapters in the thesis extend our knowledge about such non-informational feedback effects in the presence of negative convexity on the part of the dealer community.