Synthetic forwards and cost of funding in the equity derivative market

TL;DR

This paper develops a method to extract the implicit discount factor and implied funding costs from European option prices, revealing differences between markets and the actual cost of funding for major players.

Contribution

It introduces a novel technique to recover the market's implicit discount rate and funding costs solely from option prices, grounded in no-arbitrage principles.

Findings

In the EURO STOXX 50 market, the implicit interest rate matches EUR OIS.

In the S&P 500 market, an average funding cost of 34 basis points is observed.

The method provides insights into market liquidity and funding costs using only option prices.

Abstract

This study introduces a new technique to recover the implicit discount factor in the derivative market using only European put and call prices: this discount is grounded in actual transactions in active markets. Moreover, this study identifies the implied cost of funding, over OIS, of major market players. Does a liquid equity market allow arbitrage? The key idea is that the (unique) forward contract -- built using the put-call parity relation -- contains information about the market discount factor: by no-arbitrage conditions we identify the implicit interest rate such that the forward contract value does not depend on the strike. The procedure is applied to options on S&P 500 and EURO STOXX 50 indices. There is statistical evidence that, in the EURO STOXX 50 market, the implicit interest rate curve coincides with the EUR OIS one, while, in the S&P 500 market, a cost of funding of, on average, 34 basis points is added on top of the USD OIS curve.