The crypto world's hallmark is its notorious volatility, where prices can wildly swing in short timeframes. For traders, not just navigating but capitalizing on this volatility is a linchpin of ...

Ever since the seminal contributions of Bruno Dupire (1994) and Emanuel Derman and Iraj Kani (1994), who independently developed a discrete-time binomial tree version of the same result, it has been ...

David Harper is the CEO and founder of Bionic Turtle. He is also a published author with a popular YouTube channel on expert finance topics. Samantha (Sam) Silberstein, CFP®, CSLP®, EA, is an ...

After Black Monday in 1987, options implied volatilities started to display a ‘smile’ in relation to different strike prices, which models at the time could not capture. In 1994, two solutions were ...

Financial word of the day: Black-Scholes model — The Black-Scholes model remains the 2026 gold standard for pricing trillions in derivatives. It uses five key data points: stock price, strike, time, ...