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外汇交易平台比较

外汇期权

Bjerksund-Stensland Model

Will Kenton is an expert on the economy and investing laws and regulations. He previously held senior editorial roles at Investopedia and Kapitall Wire and holds a MA in Economics from The New School for Social Research and Doctor of Philosophy in English literature from NYU.

Diane Costagliola is an experienced researcher, librarian, instructor, and writer. She teaches research skills, information literacy, and writing to university students majoring in business and finance. She has published personal 外汇期权 finance articles and product reviews covering mortgages, home buying, and foreclosure.

What Is the Bjerksund-Stensland Model?

The Bjerksund-Stensland model is a closed-form option pricing model used to calculate the price of an American option. The Bjerksund-Stensland model competes with the Black-Scholes model, though the Black-Scholes model is specifically designed to price European options.

Key Takeaways

  • The Bjerksund-Stensland model is a closed-form option pricing model used to calculate the price of an American option.
  • It is designed specifically to determine the American call value at early exercise when the price of the underlying asset reaches a flat boundary.
  • The Bjerksund-Stensland model works for American options that have a continuous dividend, constant dividend yield, and discrete dividends.
  • It competes with the Black-Scholes model, though the Black-Scholes model is specifically designed to price European options.
  • Investors can use binomial and trinomial trees, which are considered “numerical” methods, as an alternative to the Bjerksund-Stensland model.

Understanding the Bjerksund-Stensland Model

The Bjerksund-Stensland model was developed in 1993 by Norwegians Petter Bjerksund and Gunnar Stensland and is used by investors to generate an estimate for the best time to execute an American option—financial derivatives that give buyers the right, but not the obligation, to buy (calls) or sell (puts) an underlying 外汇期权 asset at an agreed-upon price and 外汇期权 date.

The model is used specifically to determine the American call value at early exercise when the price of the underlying asset reaches a flat boundary and works for American options that have a continuous dividend, constant dividend yield, and discrete dividends. Bjerksund-Stensland divides the time to maturity into two periods with flat exercise boundaries — one flat boundary for each of the two periods.

American options differ from European options in that they can be exercised at any point during the contract period, rather than only on the expiration date. This feature should make the premium on an American option greater than the premium on a European option since the party selling the option is exposed to the risk of the option being exercised over the entire duration of the contract.

The Bjerksund-Stensland model takes into 外汇期权 account that options may be exercised before the expiration date, while the popular Black Scholes Method does not. This means the latter isn't really suitable for calculating the price of American options and works best when pricing more straightforward European options.

Unlike the Black Scholes model, the Bjerksund-Stensland model factors in that U.S. options may be exercised before the expiration date.

Advantages and Disadvantages of the Bjerksund-Stensland Model

The Bjerksund-Stensland model is able to complete complex calculations more quickly and efficiently compared to many other pricing methods. This was especially important because computers at the time of its inception were less powerful, and inefficient formulas could slow down calculations.

The model isn't perfect though. One flaw is that it is unable to provide the most optimal exercise strategy due to the estimates that it uses in calculations.

Special Considerations

Investors can use binomial and trinomial trees as an alternative to the Bjerksund-Stensland model. Trees are considered “numerical” methods, whereas Bjerksund-Stensland is 外汇期权 considered an approximation method. Computers are typically able to complete approximation calculations faster than they can complete numerical methods.

深度!外汇期权市场与人民币汇率的风险定价

通过一定的实证分析,笔者发现:第一,8.11汇改前实际方差和方差风险溢价均没有单独体现在人民币汇率的风险定价中,但隐含方差却纳入了人民币汇率定价。这说明当时人民币汇率波动的不确定性的确较小,方差风险溢价还没有单独成为风险来源,并且这一阶段,隐含方差对于未来的汇率具有一定预测功效。第二,8.11汇改后,双向波动市场环境下方差风险溢价体现在了人民币汇率风险定价中,说明波动率不确定性风险的重要性凸显,人民币汇率的市场化形成机制更为成熟。这与日元、瑞士法郎、 英镑 、德国马克( 欧元 推出之前)等货币的波动率风险溢价存在的国际经验一致。因此,以波动率不确定性的视角来对标世界主要货币,人民币汇率的市场化程度确实得到了有效提升。第三,8.外汇期权 11汇改前后,期权隐含波动率数据均以不同的形式体现在人民币汇率风险定价中,反映出我国外汇期权市场趋向成熟,发挥了价格发现的功能。

深度!外汇期权市场与人民币汇率的风险定价

通过一定的实证分析,笔者发现:第一,8.11汇改前实际方差和方差风险溢价均没有单独体现在人民币汇率的风险定价中,但隐含方差却纳入了人民币汇率定价。这说明当时人民币汇率波动的不确定性的确较小,方差风险溢价还没有单独成为风险来源,并且这一阶段,隐含方差对于未来的汇率具有一定预测功效。第二,8.11汇改后,双向波动市场环境下方差风险溢价体现在了人民币汇率风险定价中,说明波动率不确定性风险的重要性凸显,人民币汇率的市场化形成机制更为成熟。这与日元、瑞士法郎、 英镑 、德国马克( 欧元 推出之前)等货币的波动率风险溢价存在的国际经验一致。因此,以波动率不确定性的视角来对标世界主要货币,人民币汇率的市场化程度确实得到了有效提升。第三,8.11汇改前后,期权隐含波动率数据均以不同的形式体现在人民币汇率风险定价中,反映出我国外汇期权市场趋向成熟,发挥了价格发现的功能。

人民币外汇期权:发展方向和交易策略

行情图

人民币汇率走势双向波动的增强带动了外汇期权波动率的上下起伏。2017年人民币的快速升值带动波动率先抑后扬,2018年人民币大幅贬值带动波动率快速上冲,2019年剧烈的双边波动带动波动率先扬后抑,整体波动率水平向上抬升。以2019年 美元兑人民币 1年期ATM期权隐含波动率(1Y USD/CNY ATM VOL)为例,年初随着中美贸易形势缓和和人民币汇率的企稳回升,市场风险情绪得到逐步释放,期权隐含波动率从5.0%上方开始逐渐回落至4.3%附近。之后美元兑人民币汇率持续在低位徘徊,期权隐含波动率继续下行至年内低点3.6%附近。进入5月份中美贸易谈判恶化,人民币快速贬值,受消息面的刺激,期权隐含波动率快速反弹拉升至4.5%上方。8月份后,人民币汇率跌破“7.0”位置,期权隐含波动率急速拉升至5.5%上方,创年内新高。此后虽然美元兑人民币汇率继续上行,但由于之前波动率的快速拉升已经包含了人民币进一步贬值的预期,因此期权隐含波动率并未进一步走高。而后随着人民币向升值方向变动,期权隐含波动率逐步回落至年内低点3.8%附近。

二、当前市场环境下银行间人民币对外汇期权交易策略及风险

三、当前市场环境下的对客人民币外汇期权选择

1.“区间远期”组合。该期权组合由两笔单一期权组成,若为购汇方向的区间远期组合,该组合由一笔看涨期权和一笔看跌期权构成,两笔期权执行价格与当前同期限远期价格相等。在到期日当天,不管市场运行到哪个位置,两笔期权都将有一笔期权行权,企业能够完全地锁定到期购汇汇率,该组合能够帮助企业有效对冲汇率风险。

2.“增强/增利型的区间远期”组合。该期权组合由一个“区间远期”组合叠加一笔卖出普通期权构成。从产品表现来看,该款产品比普通“区间远期”组合风险高,相应的由于第三笔期权的存在,可以获得更好的购汇/结汇价格,因此比较适合风险偏好适中的企业。

3.“时间差购汇/结汇”组合。该期权组合由两笔单一期权组成,两笔期权的到期时间不同。企业可以通过该组合获得一定的期权费进而优化近端的结汇价格,风险保留在远端到期时点。

4.“双倍区间远期”组合。该期权组合由两笔单一期权组成,卖出期权的名义本金是买入期权的两倍。从市场表现来看,该产品风险较高,同时收益也较高,比较适合风险偏好较高的企业。