This article uses a large amount of underlying data and interpolation methods to compile a market sentiment index for the Chinese yuan (7.2785, -0.0005, -0.01%) exchange rate. The information meaning of the sentiment index is analyzed, and the relationship between the sentiment index and exchange rate risk pricing is studied based on this. It is found that the risk of volatility uncertainty has been reflected in exchange rate pricing after the 8.11 exchange rate reform, and the mechanism for the formation of the Chinese yuan exchange rate has become more mature. According to the research conclusions, it is recommended to refer to the changes in market foreign exchange sales and the US dollar index (108.4033, 0.3240, 0.30%) to further improve the implied volatility quotation.
　　
Risk pricing is one of the fundamental issues in the financial field, and risk premium is also an important source of asset excess returns. With the continuous deepening of China's foreign exchange management reform, in addition to payment methods, the investment and financing functions of foreign exchange have also been strengthened, reflected in the high level of capital account convertibility and the strong autonomy of market entities in foreign exchange settlement and sale. Due to the increasingly prominent asset allocation function of foreign exchange, issues related to the RMB exchange rate can be studied from the perspective of "return risk". The implied volatility curve of RMB USD foreign exchange options (hereinafter referred to as forex options) contains rich market information such as volatility expectations and risk preferences, providing an important entry point for the risk pricing research of RMB exchange rate. This article combines the author's existing academic achievements to analyze the relationship between implied volatility curve data and RMB exchange rate risk pricing, and explores its implications for option implied volatility pricing.
　　
1、 Using implied volatility of foreign exchange options to calculate the sentiment index of the RMB exchange rate market
　　
The VIX index is calculated based on the implied volatility of Standard&Poor's stock index options. Similarly, the principle and method can be used to calculate the market sentiment index of the RMB exchange rate, which means the expected exchange rate volatility under risk neutrality. The square of the monthly exchange rate market sentiment index is the implied variance of the exchange rate. Classic literature has proven that in theory, implicit variance is the integral value obtained by a certain method based on the option prices of all strike prices at a certain point in time. In actual calculation, the integral value needs to be converted into a discrete sum based on its mathematical characteristics, and adjusted according to foreign currency interest rates (similar to stock dividends and cash outflows). The specific formula is as follows:
　　
Due to nonlinearity and other factors, although not entirely mathematically, from an economic and financial perspective, the implied variance of exchange rates can be roughly understood as the weighted average of the squared implied volatility at each execution price. Among them, the "weight" of quotes near ATM is the highest, while the "weight" of quotes with higher and lower values is smaller.
　　
Delta values range from 0.05 to 0.95 at intervals of 0.05, representing 19 different delta implied volatility quotes. The data is sourced from Bloomberg and after 71 rounds of cubic spline interpolation, the implied variance of the exchange rate is calculated. Among them, the cubic spline interpolation method uses multiple cubic functions to fit the implied volatility curve, and interpolates according to the fitted curve. And the first-order and second-order continuous differentiable cubic functions have smooth curves and good mathematical properties. Due to the use of a large amount of basic data and intensive interpolation, the calculation method in this article is relatively rigorous and accurate. After annualizing the implied variance and then square root, it can be converted into the RMB exchange rate market sentiment index, representing the expected exchange rate volatility for the next month at the end of each month.
　　
The measurement results indicate that after the 8.11 exchange rate reform, the absolute value and volatility of the RMB exchange rate sentiment index have significantly increased. There is no stable relationship between the exchange rate sentiment index and the actual fluctuation of the exchange rate. Sometimes, the actual operation of exchange rates will have a pro cyclical response to the expected exchange rate volatility in the early stage. The sentiment index in August 2018 was 6.39%, a nearby high point, and the RMB entered a phase of depreciation in the fourth quarter thereafter; A similar situation occurred in November 2020, with an sentiment index of 7.3%, but corresponding to a period of appreciation. Sometimes, due to the high elasticity of exchange rates, after the release of upward and downward pressure, the sentiment index actually decreases. The sentiment index in May 2019 was 2.39%, which is a nearby low point. At that time, the RMB exchange rate "broke 7", playing an automatic regulatory role in the internal and external economic and financial conditions, and market expectations tended to stabilize instead.
　　
2、 Risk Pricing Analysis of Renminbi Exchange Rate
　　
According to the asset pricing research approach of "return risk", risk factors may be reflected in the excess returns of assets as compensation for taking on risks. The volatility risk of asset prices is one of the most common risk factors. The author used high-frequency data of spot exchange rates to calculate the actual volatility (variance) of the RMB exchange rate. In addition, the risk of volatility uncertainty is another risk factor for the RMB exchange rate. For example, before the exchange rate reform from 7.21 to 8.11, based on the principles of "active, gradual, and controllable", the overall appreciation rate of the RMB against the US dollar was relatively stable, and the market's expectations of RMB exchange rate volatility were not likely to deviate too much (such as an annual appreciation rate of 3% to 5%), resulting in low uncertainty in exchange rate volatility. After the 8.11 exchange rate reform, the two-way fluctuation of the RMB exchange rate has continued to increase, and the volatility has greater uncertainty than before.
　　
Implied variance is based on risk neutral pricing, and risk neutral investors do not need to receive risk compensation for taking on risks. So, the difference between the expected variance under risk neutrality and actual risk preference reflects the risk compensation for future volatility uncertainty. The financial term for the difference between the two is called variance risk premium, which can serve as a proxy variable for the uncertainty risk of exchange rate fluctuations. The variance risk premium is usually positive. This is because the expected volatility under risk neutrality corresponds to the risk-free rate, while the actual volatility under risk aversion in reality corresponds to a higher yield than the risk-free rate. Generally speaking, the higher the yield, the higher the call option price; The higher the volatility, the higher the call option price. Therefore, the expected volatility (variance) under risk neutrality will be higher than the actual volatility (variance) under risk aversion. Under the assumption of rational expectations, the variance risk premium is the implied variance of the exchange rate minus the actual variance, and the sum of the actual variance and the variance risk premium is exactly equal to the implied variance. Therefore, the implied volatility data of options includes two types of risks - exchange rate volatility risk and exchange rate volatility uncertainty risk.
　　
Through certain empirical analysis, the author found that: firstly, before the 8.11 exchange rate reform, both the actual variance and variance risk premium were not separately reflected in the risk pricing of the RMB exchange rate, but the implicit variance was included in the RMB exchange rate pricing. This indicates that the uncertainty of RMB exchange rate fluctuations was indeed relatively small at that time, and variance risk premium had not yet become a separate source of risk. Moreover, at this stage, implicit variance had a certain predictive effect on future exchange rates. Secondly, after the 8.11 exchange rate reform, the variance risk premium in the two-way volatile market environment is reflected in the pricing of RMB exchange rate risk, indicating the importance of volatility uncertainty risk and a more mature market-oriented mechanism for the formation of RMB exchange rate. This is consistent with international experience regarding the volatility risk premium of currencies such as the Japanese yen, Swiss franc, British pound (1.2286, -0.0038, -0.31%), and German mark (before the introduction of the euro (1.0380, -0.0036, -0.35%)). Therefore, from the perspective of volatility uncertainty, the marketization level of the RMB exchange rate has indeed been effectively improved by benchmarking against major world currencies. Thirdly, before and after the 8.11 exchange rate reform, the implied volatility data of options were reflected in different forms in the pricing of RMB exchange rate risk, reflecting the maturity of China's foreign exchange options market and playing the role of price discovery.
　　
3、 Some insights on implied volatility pricing
　　
Based on the above analysis, participants in the foreign exchange market can form implied volatility quotes from two perspectives. One is to report the implied volatility based on the influencing factors of the RMB exchange rate sentiment index; The second is to predict the actual volatility of future exchange rates, and then report the volatility risk premium based on the influencing factors of the volatility risk premium (the difference between the RMB exchange rate sentiment index and the actual volatility, which is consistent with the economic significance and variance risk premium). The sum of the two forms the implied volatility quotation under risk neutrality. To study the influencing factors of the RMB exchange rate sentiment index and exchange rate volatility risk premium after the 8.11 exchange rate reform, the author considered the following variables: (1) economic fundamentals, including China PMI, US manufacturing PMI, and US non manufacturing PMI; (2) International balance of payments situation, including customs import and export surplus and short-term capital flows (foreign exchange accumulation - trade surplus - actual utilization of FDI); (3) The foreign exchange settlement and sale behavior in the proxy market can be measured by the bank's proxy settlement/collection exchange rate and the foreign exchange sales/payment rate. The former refers to the ratio of the bank's proxy settlement to the proxy collection in the current period, while the latter refers to the ratio of the bank's proxy sales to the proxy payment in the current period; (4) The US dollar index.
　　
A simple empirical analysis found that, firstly, only the sales/payment rate has a significant impact on the sentiment index of the RMB exchange rate, and the relationship between the two is negative. After the exchange rate reform on August 11th, there were several stages of depreciation of the RMB, such as from the end of 2016 to the beginning of 2017, in the fourth quarter of 2018, and in May 2019, the RMB exchange rate faced three pressures of "breaking 7", and in August 2019, it even achieved "breaking 7". The intensification of foreign exchange sales behavior will increase depreciation pressure, but when transmitted to expectations, it will result in a narrowing of expected exchange rate volatility. This reflects market rationality, believing that the exchange rate can play an automatic regulatory role and the subsequent exchange rate trend will return to a reasonable level. Looking at it from a different perspective, when the RMB shows a certain appreciation trend, an increase in the exchange rate for selling/paying foreign exchange will alleviate the pressure of appreciation and prevent further divergence of volatility expectations. However, the sentiment index of the RMB exchange rate is not sensitive to the settlement situation. In addition, the sentiment index of the RMB exchange rate also has common autoregressive characteristics. Secondly, only the absolute value of changes in the US dollar index has a significant impact on the volatility risk premium, and the relationship between the two is positive. The US dollar exchange rate is one of the "barometers" of global macroeconomic and financial fluctuations, and has been proven by many literature to be an important pricing factor for currency excess returns. This article also found that external factors affecting the volatility of the US dollar index can indeed increase the risk of volatility uncertainty, thereby affecting the risk pricing of the RMB exchange rate. Therefore, in the short term, the recent sales of foreign exchange in the proxy market and fluctuations in the US dollar index are important references for reporting the sentiment index and volatility risk premium of the RMB exchange rate, while the correlation between economic fundamentals and international balance of payments is relatively weak. Of course, the implied volatility quotation based on a certain delta or strike price also needs to be adjusted according to factors such as predicting the direction of exchange rate changes (implied volatility curve shape). The sentiment index of RMB exchange rate and other influencing factors of volatility risk premium also need to be further explored.